The perpendicular distance of a point from the x-axis is 2 units and the perpendicular distance from the y-axis is 3 units. Write the coordinates of the point if it lies in the:

(i) I quadrant    (ii) II quadrant
(iii)    III quadrant    (iv) IV quadrant


(i) (3, 2)
(ii) (-3, 2)
(iii) (-3, -2)
(iv) (3, -2)

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Plot the point P(2, -6) on graph paper and from it draw PM and PN as perpendiculars to x-axis and y-axis respectively. Write the coordinates of the points M and N.


M → (2, 0)N → (0, -6)

M → (2, 0)
N → (0, -6)

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A point lies on x-axis at a distance of 9 units from y-axis. What are its coordinates? What will be its coordinates if it lies on y-axis at a distance of 9 units from x-axis.

(0, 9), (0, -9).
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In figure given below, triangle AOB with coordinates of A and O as (4, 0) and (0, 0), find the coordinates of B.


In right triangle AOB OA2 + OB2 = AB2
| By Pythagoras Theorem
⇒ 42 + OB2 = 52
⇒ 16 + OB2 = 25
⇒ OB2 = 9
⇒    OB = 3
⇒    B → (0, 3)

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In figure, ∆ABC and ∆ABD are equilateral triangles. Find the coordinates of points C and D.


∵ ∆ABC is an equilateral triangle
∴AC = BC = AB
⇒ BC = AB
⇒ BC = 2a
In right triangle COB,
OB2 + OC2 = BC

rightwards double arrow space space a2 + OC= (2a)2

rightwards double arrow  OC2 + 3a2

rightwards double arrow  OC space equals space square root of 3 space straight a

therefore space space space space space space space space space space straight C rightwards arrow space space left parenthesis 0 comma space square root of 3 space straight a right parenthesis

Similarly,   straight D space rightwards arrow space left parenthesis 0 comma space minus square root of 3 space straight a right parenthesis

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