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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.
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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)
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