Question

The coordinates of the point P are (-3, 2). Find the coordinates of the point Q which lies on the line joining P and origin such that OP = OQ.

Answer 1

Coordinates of P = (-3, 2)
Coordinates of origin = (0, 0)
Let the coordinates of Q = (x, y)
Given that OP = OQ ⇒ O is the midpoint of the line joining P and Q
Midpoint of the line segment joining (x₁, y₁) and (x₂, y₂) = ($\frac{x_1+x_2}{2}$, $\frac{y_1+y_2}{2}$)​​​​​​​

Midpoint of PQ = ($\frac{-3+x}{2}$, $\frac{2+y}{2}$) ​​​ = (0, 0)

$\frac{-3+x}{2}$= 0 ⇒ x = 3

$\frac{2+y}{2}$= 0 ⇒ y = -2
The point Q is (3,-2)