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 `(x_1,y_1)` and `(x_2, y_2)` are given as two points, then the co-ordinates of the midpoint of the line joining these two points is given as

`(x_m,y_m) = ((x_1 + x_2)/2, (y_1 + y_2)/2)`

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 OP = OQ

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

So we have that `(x_m,y_m) = (0,0)`

Substituting the values in the earlier mentioned formula we get,

`(x_m,y_m) = ((-3 + x)/2, (2 + y)/2)`

`(0,0) = ((-3 + x)/2, (2 + x)/2)`

Equating individually we have, x = 3 and y = -2

Thus the co−ordinates of the point ‘*Q*’ is (3, -2)