**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.

**Solution:**

If $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ are given as two points, then the co-ordinates of the midpoint of the line joining these two points is given as

$\left(x_{m}, y_{m}\right)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

It is given that the point ‘*P*’ has co-ordinates (*−*3*, *2)

Here we are asked to find out the co-ordinates of point ‘*Q*’ which lies along the line joining the origin and point ‘*P*’. Thus we can see that the points ‘*P*’, ‘*Q*’ and the origin are collinear.

Let the point ‘*Q*’ be represented by the point (*x, y*)

Further it is given that the

This implies that the origin is the midpoint of the line joining the points ‘*P*’ and ‘*Q*’.

So we have that

Substituting the values in the earlier mentioned formula we get,

$\left(x_{m}, y_{m}\right)=\left(\frac{-3+x}{2}, \frac{2+y}{2}\right)$

$(0,0)=\left(\frac{-3+x}{2}, \frac{2+y}{2}\right)$

Equating individually we have, and.

Thus the co−ordinates of the point ‘*Q*’ is