Students can cross-reference their work with Class 11 OP Malhotra Solutions Chapter 15 Basic Concepts of Points and their Coordinates Ex 15(a) to ensure accuracy.
S Chand Class 11 ICSE Maths Solutions Chapter 15 Basic Concepts of Points and their Coordinates Ex 15(a)
Question 1.
Find the coordinates of the points shown on the graph in Fig. given below :
(i) P
(ii) Q
(iii) O
(iv) R
(v) S
(vi) A
(vii) L
(viii) M
Solution:
(i) Clearly point P lies on x-axis and is at a distance of 3 units from O on left side of y-axis.
∴ Coordinates of point P are (-3, 0).
(ii) Point Q is situated at a 2 units distance from O on +ve direction of x-axis and moves at a 5 units distance along +ve y-axis.
∴ Coordinates of Q are (2, 5)
(iii) Point O represents the origin and its coordinates are (0, 0).
(iv) Point R is situated at a distance 3 units in -ve direction of x-axis and then moves at a distance of 5 units in -ve direction of y-axis.
∴ Coordinates of R are (-3, -5).
(v) Point S lies on +ve direction of x-axis at a distance of 3 units from O.
∴ Coordinates of S are (3, 0).
(vi) Point A is situated at a distance of 4 units on +ve direction of x-axis and then moves at a distance of 3 in -ve direction of y-axis. Then the coordinates of A are (4, -3).
(vii) Point L is situated at a distance of 4 units on -ve direction of x-axis and then moves 2 units distance in -ve direction of y-axis.
∴ Coordinates of L are (-4, -2).
(viii) Point M is situated on y-axis at a distance of 2 units in +ve direction of y-axis. Then coordinates of point M are (0, 2).
Question 2.
Plot the points (2, 3),(-5, -7),(-4, 6), (0, 8),(-5, 0) on the graph paper.
Solution:
The point P(2, 3) is of the form (+, +) i.e. lies in first quadrant. The point P is at a distance of 2 units along +ve x-axis and then moves 3 units along +ve direction of y-axis.
The point (-5, -7) is situated at a distance of 5 units in-ve direction of x-axis and then moves 7 units in -ve direction of y-axis.
The point (-4, 6) is situated at a distance of 4 units in -ve direction of x-axis and then moves at a distance of 6 units in +ve direction of y-axis.
Clearly the point (0, 8) is situated on y-axis at a distance of 8 units from origin.
The point (-5, 0) is situated on-ve direction of x-axis and is at a distance of 5 units from origin O.
Question 3.
Where will a point lie if (i) its ordinate is zero, (ii) its abscissa is zero?
Solution:
(i) We know that, a point P(x, 0) is always lies on x-axis. ∴ the point with its ordinate is zero is always lies on x-axis.
(ii) We know that a point P(0, y) is always lies on y-axis. Thus the point with its abscissa is 0 is always lies on y-axis.
Question 4.
Where will a point lie if (i) the abscissa equals the ordinate; (ii) the positive abscissa equals the negative of the positive ordinate?
Solution:
(i) Clearly when the abscissa of point = ordinate of point
⇒ x = y
∴ the point (x, y) is always lies on angular bisectors of the axes.
(ii) given positive abscissa = negative ordinate of point
⇒ x = -y; where x, y > 0
Clearly the point (x, -x) lies in fourth quadrant on the angular bisector of the axes.
