Question

The mid-point of the segment AB, as shown in diagram, is C(4, –3). Write down the co-ordinates of A and B.

Answer 1

Since, point A lies on x-axis, let the co-ordinates of point A be (x, 0).

Since, point B lies on y-axis, let the co-ordinates of point B be (0, y).

Given, mid-point of AB is C(4, −3).

∴ `(4, -3) = ((x + 0)/2, (0 + y)/2)`

`=> (4 - 3) = (x/2, y/2)`

`=> 4 = x/2` and `-3 = y/2`

`=>` x = 8 and y = −6

Thus, the co-ordinates of point A are (8, 0) and the co-ordinates of point B are (0, −6).