ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry

EXERCISE 19.1

Question 1.
Find the co-ordinates of points whose
(i) abscissa is 3 and ordinate -4.
(ii) abscissa is – \(\frac { 3 }{ 2 }\)and ordinate 5.
(iii) whose abscissa is -1\(\frac { 2 }{ 3 }\) and ordinate -2 \(\frac { 1 }{ 4 }\) .
(iv) whose ordinate is 5 and abscissa is -2
(v) whose abscissa is -2 and lies on x-axis.
(vi) whose ordinate is \(\frac { 3 }{ 2 }\) and lies on y-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q1.1

Question 2.
In which quadrant or on which axis each of the following points lie?
(-3, 5), (4, -1) (2, 0), (2, 2), (-3, -6)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q2.1

Question 3.
Which of the following points lie on
(i) x-axis? (ii) y-axis?
A (0, 2), B (5, 6), C (23, 0), D (0, 23), E (0, -4), F (-6, 0), G (√3,0)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q3.1

Question 4.
Plot the following points on the same graph paper :
A (3, 4), B (-3, 1), C (1, -2), D (-2, -3), E (0, 5), F (5, 0), G (0, -3), H (-3, 0).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q4.1

Question 5.
Write the co-ordinates of the points A, B, C, D, E, F, G and H shown in the adjacent figure.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q5.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q5.2

Question 6.
In which quadrants are the points A, B, C and D of problem 3 located ?
Solution:
A Lies in the first quadrant, B lies on x-axis C lies in the third quadrant and D lies in the fourth quadrant.

Question 7.
Plot the following points on the same graph paper :
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q7.2

Question 8.
Plot the following points on the same graph paper.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q8.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q8.2

Question 9.
Plot the following points and check whether they are collinear or not:
(i) (1,3), (-1,-1) and (-2,-3)
(ii) (1,2), (2,-1) and (-1, 4)
(iii) (0,1), (2, -2) and (\(\frac { 2 }{ 3 }\) ,0)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q9.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q9.2

Question 10.
Plot the point P(-3, 4). Draw PM and PN perpendiculars to x-axis and y-axis respectively. State the co-ordinates of the points M and N.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q10.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q10.2

Question 11.
Plot the points A (1,2), B (-4,2), C (-4, -1) and D (1, -1). What kind of quadrilateral is ABCD ? Also find the area of the quadrilateral ABCD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q11.1

Question 12.
Plot the points (0,2), (3,0), (0, -2) and (-3,0) on a graph paper. Join these points (in order). Name the figure so obtained and find the area of the figure obtained.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q12.2

Question 13.
Three vertices of a square are A (2,3), B(-3, 3) and C (-3, -2). Plot these points on a graph paper and hence use it to find the co-ordinates of the fourth vertex. Also find the area of the square.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q13.1

Question 14.
Write the co-ordinates of the vertices of a rectangle which is 6 units long and 4 units wide if the rectangle is in the first quadrant, its longer side lies on the x-axis and one vertex is at the origin.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q14.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q14.2

Question 15.
Repeat problem 12 assuming that the rectangle is in the third quadrant with all other conditions remaining the same.
Solution:
A rectangle which is 6 unit long and 4 units wide and this rectangle is in the third quadrant.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q15.1

Question 16.
The adjoining figure shows an equilateral triangle OAB with each side = 2a units. Find the coordinates of the vertices.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q16.2

Question 17.
In the given figure, APQR is equilateral. If the coordinates of the points Q and R are (0, 2) and (0, -2) respectively, find the coordinates of the point P.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q17.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q17.2

EXERCISE 19.2

Question 1.
Draw the graphs of the following linear equations :
(i) 2x + + 3 = 0
(ii) x- 5y- 4 = 0
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q1.2

Question 2.
Draw the graph of 3y= 12 – 2x. Take 2cm = 1 unit on both axes.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q2.1

Question 3.
Draw the graph of 5x + 6y – 30 = 0 and use it to find the area of the triangle formed by the line and the co-ordinate axes.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q3.1

Question 4.
Draw the graph of 4x- 3y + 12 = 0 and use it to find the area of the triangle formd by the line and the co-ordinate axes. Take 2 cm = 1 unit on both axes.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q4.2

Question 5.
Draw the graph of the equation y = 3x – 4. Find graphically.
(i) the value of y when x = -1
(ii) the value of x when y = 5.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q5.2

Question 6.
The graph of a linear equation in x and y passes through (4, 0) and (0, 3). Find the value of k if the graph passes through (A, 1.5).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q6.1

Question 7.
Use the table given alongside to draw the graph of a straight line. Find, graphically the values of a and b.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q7.2

EXERCISE 19.3

Question 1.
Solve the following equations graphically: 3x – 2y = 4, 5x – 2y = 0
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q1.2

Question 2.
Solve the following pair of equations graphically. Plot at least 3 points for each straight line 2x – 7y = 6, 5x – 8y = – 4
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q2.2

Question 3.
Using the same axes of co-ordinates and the same unit, solve graphically.
x+y = 0, 3x – 2y = 10
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q3.2

Question 4.
Take 1 cm to represent 1 unit on each axis to draw the graphs of the equations 4x- 5y = -4 and 3x = 2y – 3 on the same graph sheet (same axes). Use your graph to find the solution of the above simultaneous equations.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q4.2

Question 5.
Solve the following simultaneous equations graphically, x + 3y = 8, 3x = 2 + 2y
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q5.2

Question 6.
Solve graphically the simultaneous equations 3y = 5 – x, 2x = y + 3 (Take 2cm = 1 unit on both axes).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q6.2

Question 7.
Use graph paper for this question.
Take 2 cm = 1 unit on both axes.
(i) Draw the graphs of x +y + 3 = 0 and 3x-2y + 4 = 0. Plot only three points per line.
(ii) Write down the co-ordinates of the point of intersection of the lines.
(iii) Measure and record the distance of the point of intersection of the lines from the origin in cm.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q7.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q17.5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q17.4

Question 8.
Solve the following simultaneous equations graphically :
2x-3y + 2 = 4x+ 1 = 3x – y + 2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q8.1

Question 9.
Use graph paper for this question.
(i) Draw the graphs of 3x -y – 2 = 0 and 2x + y – 8 = 0. Take 1 cm = 1 unit on both axes and plot three points per line.
(ii) Write down the co-ordinates of the point of intersection and the area of the traingle formed by the lines and the x-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q9.1

Question 10.
Solve the following system of linear equations graphically : 2x -y – 4 = 0, x + y + 1 = 0. Hence, find the area of the triangle formed by these lines and the y-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q10.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q10.2

Question 11.
Solve graphically the following equations: x + 2y = 4, 3x – 2y = 4
Take 2 cm = 1 unit on each axis. Write down the area of the triangle formed by the lines and the x-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q11.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q11.3

Question 12.
On graph paper, take 2 cm to represent one unit on both the axes, draw the lines : x + 3 = 0, y –  2 = 0, 2x + 3y = 12 .
Write down the co-ordinates of the vertices of the triangle formed by these lines.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q12.2

Question 13.
Find graphically the co-ordinates of the vertices of the triangle formed by the lines y = 0, y – x and 2x + 3y= 10. Hence find the area of the triangle formed by these lines.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q13.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q13.3

EXERCISE 19.4

Question 1.
Find the distance between the following pairs of points :
(i) (2, 3), (4, 1)
(ii) (0, 0), (36, 15)
(iii) (a, b), (-a, -b)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q1.2

Question 2.
A is a point on y-axis whose ordinate is 4 and B is a point on x-axis whose abscissa is -3. Find the length of the line segment AB.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q2.1

Question 3.
Find the value of a, if the distance between the points A (-3, -14) and B (a, -5) is 9 units.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q3.2

Question 4.
(i) Find points on the x-axis which are at a distance of 5 units from the point (5, -4).
(ii) Find points on the y-axis are at a distance of 10 units from the point (8, 8) ?
(iii) Find points (or points) which are at a distance of √10 from the point (4, 3) given that the ordinate of the point or points is twice the abscissa.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q4.2

Question 5.
Find the point on the x-axis which, is equidistant from the points (2, -5) and (-2, 9).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q5.2

Question 6.
Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q6.1

Question 7.
If Q (0, 1) is equidistant from P (5, -3) and R (x, 6) find the values of x.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q7.1

Question 8.
Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q8.2

Question 9.
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from the points Q (2, -5) and U (-3, 6), then find the coordinates of P.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q9.1

Question 10.
If the points A (4,3) and B (x, 5) are on a circle with centre C (2, 3), find the value of x.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q10.1

Question 11.
If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5), then find the value of p.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q11.1

Question 12.
Using distance formula, show that (3, 3) is the centre of the circle passing through the points (6, 2), (0, 4) and (4, 6).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q12.1

Question 13.
The centre of a circle is C (2α – 1, 3α + 1) and it passes through the point A (-3, -1). If a diameter of the circle is of length 20 units, find the value(s) of α.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q13.2

Question 14.
Using distance formula, show that the points A (3, 1), B (6, 4) and C (8, 6) are coliinear.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q14.1

Question 15.
Check whether the points (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q15.1

Question 16.
Name the type of triangle formed by the points A (-5, 6), B (-4, -2) and (7, 5).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q16.1

Question 17.
Show that the points (1, 1), (- 1, – 1) and (-√3,√3) form an equilateral triangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q17.1

Question 18.
Show that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q18.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q18.2

Question 19.
The points A (0, 3), B (- 2, a) and C (- 1, 4) are the vertices of a right angled triangle at A, find the value of a.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q19.1

Question 20.
Show that the points (0, – 1), (- 2, 3), (6, 7) and (8, 3), taken in order, are the vertices of a rectangle. Also find its area.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q20.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q20.2

Question 21.
If P (2, -1), Q (3, 4), R (-2, 3) and S (-3, -2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q21.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q21.2

Question 22.
Prove that the points A (2, 3), B {-2, 2), C (-1, -2) aqd D (3, -1) are the vertices of a square ABCD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q22.2

Question 23.
Name the type of quadrilateral formedby the following points and give reasons for your answer :
(i) (-1, -2), (1, 0), (-1, 2), (-3, 0)
(ii) (4, 5), (7, 6), (4, 3), (1, 2)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q23.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q23.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q23.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q23.4

Question 24.
Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, -2) and (2, -2). Also, find its circumradius.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q24.1

Question 25.
If two opposite vertices of a square are (3, 4) and (1, -1), find the coordinates of the other two vertices.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q25.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q25.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q25.3

Multiple Choice Questions

Choose the correct answer from the given four options (1 to 16):
Question 1.
Point (-3, 5) lies in the
(a) first quadrant
(b) second quadrant
(c) third quadrant
(d) fourth quadrant
Solution:
Point (-3, 5) lies in second quadrant, (b)

Question 2.
Point (0, -7) lies
(a) on the x-axis
(b) in the second quadrant
(c) on the y-axis
(d) the fourth quadrant
Solution:
Point (0, -7) lies on y-axis (as x = 0) (c)

Question 3.
Abscissa of a point is positive in
I and II quadrants
I and IV quadrants
I quadrant only
II quadrant only
Solution:
Abscissa of a point is positive in first and fourth quadrants. (b)

Question 4.
The point which lies ony-axis at a distance of 5 units in the negative direction of y- axis is
(a) (0, 5)
(b) (5, 0)
(c) (0, -5)
(d) (-5, 0)
Solution:
(0, -5) is the required point. (c)

Question 5.
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of perpendicular lies on the negative direction of x-axis, then the point P has
(a) x-coordinate = -5
(b) y-coordinate = 5 only
(c) y-coordinate = -5 only
(d) y-coordinate = 5 or -5
Solution:
Perpendicular distance for a point P on x- axis in negative direction.
It will has y = 5 and x = -5 (d)
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q5.1

Question 6.
The points whose abscissa and ordinate have different signs will lie in
(a) I and II quadrants
(b) II and III quadrants
(c) I and III quadrants
(d) II and IV quadrants
Solution:
Point which has abscissa and ordinate having different signs will lie in second and fourth quadrants. (d)

Question 7.
The points (-5, 2) and (2, -5) lie in
(a) same quadrant
(b) II and III quadrants respectively
(c) II and IV quadrants respectively
(d) IV and II quadrants respectively
Solution:
Points (-5, 2) and (2, -5) lie in second and fourth quadrants respectively. (b)

Question 8.
If P (-1,1), Q (3, -4), R (1, -1), S (-2, -3) and T (-4, 4) are plotted on the graph paper, then point(s) in the fourth quadrant are
(a) P and T
(b) Q and R
(c) S only
(d) P and R
Solution:
Points P (-1, 1), Q (3, -4), R (1, -1), S (-2, -3) and T (-4, 4) are plotted on graph The points in 4th quadrant are Q and R (b)

Question 9.
On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4) and joining OA, AB, BC and CO which of the following figure is obtained?
(a) Square
(b) Rectangle
(c) Trapezium
(d) Rhombus
Solution:
On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4)
OA, AB, BC and CO are joined
The figure so formed will a rectangle (b)

Question 10.
Which of the following points lie on the graph of the equation :
3x-5y + 7 = 0?
(a) (1, -2)
(b) (2, 1)
(c) (-1, 2)
(d) (1, 2)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q10.1

Question 11.
The pair of equation x – a and y = b graphically represents lines which are
(a) parallel
(b) intersecting at (b, a)
(c) coincident
(d) intersecting at (a, b)
Solution:
x = a, y = 6
Which are intersecting at (a, b) (d)

Question 12.
The distance of the point P (2, 3) from the x>axis is
(a) 2 units
(b) 3 units
(c) 1 unit
(d) 5 units
Solution:
The distance of the point P (2, 3) from x- axis is 3 units (as y = 3). (b)

Question 13.
The distance of the point P (-4, 3) from the y-axis is
(a) 5 units
(b) -4 units
(c) 4 units
(d) 3 units
Solution:
The distance of the point P (-4, 3) from y- axis will be 4 units. (c)

Question 14.
The distance of the point P (-6, 8) from the origin is
(a) 8 units
(b) 2\(\sqrt { 7 }\) units
(c) 10 units
(d) 6 units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q14.1

Question 15.
The distance between the points A (0, 6) and B (0, -2) is
(a) 6 units
(b) 8 units
(c) 4 units
(d) 2 units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q15.1

Question 16.
The distance between the points (0, 5) and (-5, 0) is
(a) 5 units
(b) 5\(\sqrt { 2 }\)units
(c) 2 \(\sqrt { 7 }\) units
(d) 10 units
Solution:
The distance between the points (0, 5) and (-5, 0) is
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q16.1

Question 17.
AOBC is a rectangle whose three vertices are A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is
(a) 5 units
(b) 3 units
(c) \(\sqrt { 34 }\) units
(d) 4 units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q17.1

Question 18.
If the distance between the points (2, -2) and (-1, x) is S units, then one of the value of x is
(a) -2
(b) 2
(c) -1
(d) 1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q18.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q18.2

Question 19.
The distance between the points (4, p) and (1, 0) is 5 units, then the value of p is
(a) 4 only
(b) -4 only
(c) ±4
(d) 0
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q19.1

Question 20.
The points (-4, 0), (4, 0) and (0, 3) are the vertices of a
(a) right triangle
(b) isosceles triangle
(c) equilateral triangle
(d) scalene triangle
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q20.1

Question 21.
The area of a square whose vertices are A (0, -2), B (3, 1), C (0, 4) and D (-3, 1) is
(a) 18 sq. units
(b) 15 sq. units
(c) \(\sqrt { 18 }\) sq. units
(d) \(\sqrt { 15 }\) sq. units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q21.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q21.2

Question 22.
In the given figure, the area of the triangle ABC is
(a) 15 sq. units
(b) 10 sq. units
(c) 7.5 sq. units
(d) 2.5 sq. units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q22.2

Question 23.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5 units
(b) 12 units
(c) 11 units
(d) 7 + \(\sqrt { 5 }\) units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q23.1

Question 24.
If A is a point on the .y-axis whose ordinate is 5 and B is the point (-3, 1), then the length of AB is
(a) 8 units
(b) 5 units
(c) 3 units
(d) 25 units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q24.1

Question 25.
The point A (9, 0), B (9, 6), C (-9, 6) and D (-9, 0) are the vertices of a
(a) rectangle
(b) square
(c) rhombus
(d) trapezium
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q25.1

Chapter Test

Question 1.
Three vertices of a rectangle are A (2, -1), B (2, 7) and C(4, 7). Plot these points on a graph and hence use it to find the co-ordinates of the fourth vertex D Also find the co-ordinates of
(i) the mid-point of BC
(ii) the mid point of CD
(iii) the point of intersection of the diagonals. What is the area of the rectangle ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q1.1

Question 2.
Three vertices of a parallelogram are A (3, 5), B (3, -1) and C (-1, -3). Plot these points on a graph paper and hence use it to find the coordinates of the fourth vertex D. Also find the coordinates of the mid-point of the side CD. What is the area of the parallelogram?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q2.2

Question 3.
Draw the graphs of the following linear equations.
(i) y = 2x – 1
(ii) 2x + 3y = 6
(iii) 2x – 3y = 4.
Also find slope and y-intercept of these lines.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q3.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q3.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q3.4

Question 4.
Draw the graph of the equation 3x – 4y = 12. From the graph, find :
(i) the value of y when x = -4
(ii) the value of x when y = 3.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q4.2

Question 5.
Solve graphically, the simultaneous equations: 2x – 3y = 7; x + 6y = 11.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q5.2

Question 6.
Solve the following system of equations graphically: x – 2y – 4 = 0, 2x + .y – 3 = 0.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q6.2

Question 7.
Using a scale of l cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x:+ 10,y = 5;c-15. From the graph, find
(i) the coordinates of the point where the two lines intersect.
(ii) the area of the triangle between the lines and the x-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q7.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q7.2

Question 8.
Find, graphically, the coordinates of the vertices of the triangle formed by the lines : 8y – 3x + 7 = 0, 2x-y + 4 = 0 and 5x + 4y = 29.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q8.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q8.3

Question 9.
Find graphically the coordinates of the vertices of the triangle formed by the lines y-2 = 0,2y + x = 0 and y + 1 = 3(x – 2). Hence, find the area of the triangle formed by these lines.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q9.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q9.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q9.3

Question 10.
A line segment is of length 10 units and one of its end is (-2,3). If the ordinate of the other end is 9, find the abscissa of the other end.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q10.1

Question 11.
A (-4, -1), B (-1, 2) and C (a, 5) are the vertices of an isosceles triangle. Find the value of a, given that AB is the unequal side.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q11.2

Question 12.
If A (-3, 2), B (a, p) and C (-1, 4) are the vertices of an isosceles triangle, prove that α + β = 1, given AB = BC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q12.2

Question 13.
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right angled isosceles triangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q13.2

Question 14.
(i) Show that the points (2, 1), (0,3), (-2, 1) and (0, -1), taken in order, are the vertices of a square. Also find the area of the square.
(ii) Show that the points (-3, 2), (-5, -5), (2, -3) and (4, 4), taken in order, are the vertices of rhombus. Also find its area. Do the given points form a square?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q14.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q14.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q14.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q14.4

Question 15.
The ends of a diagonal of a square have co-ordinates (-2, p) and (p, 2). Find p if the area of the square is 40 sq. units.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q15.1

Question 16.
What type of quadrilateral do the points A (2, -2), B (7, 3), C (11, -1) and D (6, -6), taken in the order, form?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q16.2

Question 17.
Find the coordinates of the centre of the circle passing through the three given points A (5, 1), B (-3, -7) and C (7, -1).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q17.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q17.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q17.3

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