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Question
AB is a diameter of a circle with centre C = (- 2, 5). If A = (3, – 7). Find
(i) the length of radius AC
(ii) the coordinates of B.
Solution
(i) AC = `Sqrt((3 + 2)^2 + (-7 - 5)^2)` ...(Distance Formula)
= `sqrt( 25 + 144)`
Radius = `sqrt169` = 13 units
(ii) As 'c' is midpoint of AB
`-2 = (3 + x)/2` ...(midpoint theorem)
or - 4 = 3 + x
x = - 7
and 5 = `(- 7 + y)/2`
and 10 = - 7 + y
and y = 17
∴ B(-7, 17)
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