Question

AB is a diameter of a circle with centre C = (–2, 5). If A = (3, –7), find

1. the length of radius AC.
2. the coordinates of B.

Answer 1

i. Radius AC = `sqrt((3 + 2)^2 + (-7 - 5)^2)`

= `sqrt(5^2 + (-12)^2)`

= `sqrt(25 + 144)`

= `sqrt(169)`

= 13 units

ii. Let the co-ordinates of B be (x, y)

Using mid-point formula, we have

`-2 = (3 + x)/2` and `5 = (-7 + y)/2`

`=>` −4 = 3 + x and 10 = –7 + y

`=>` x = –7 and y = 17

Thus, the coordinates of B are (–7, 17)