Question

Given a line ABCD in which AB = BC = CD, B = (0, 3) and C = (1, 8). Find the co-ordinates of A and D.

Answer 1

Given, AB = BC = CD

So, B is the mid-point of AC.

Let the co-ordinates of point A be (x, y).

∴ `(0, 3) = ((x + 1)/2, (y + 8)/2)`

`=> 0 = (x + 1)/2` and `3 = (y + 8)/2`

`=>` 0 = x + 1 and 6 = y + 8

`=>` –1 = x and –2 = y

Thus, the co-ordinates of point A are (–1, –2).

Also, C is the mid-point of BD.

Let the co-ordinates of point D be (p, q).

∴ `(1, 8) = ((0 + p)/2, (3 + q)/2)`

`=> 1 = (0 + p)/2` and `8 = (3 + q)/2`

`=>` 2 = 0 + p and 16 = 3 + q

`=>` 2 = p and 13 = q

Thus, the co-ordinates of point D are (2, 13).