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Question
AB is a diameter of a circle with centre C = (–2, 5). If A = (3, –7), find
- the length of radius AC.
- the coordinates of B.
Solution
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)
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