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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.
Solution
1) Radius AC = `sqrt((3+2)^2 + (-7-5)^2)`
`= sqrt((5)^2 + (-12)^2)`
`=sqrt(25 + 144)`
`=sqrt(169)`
= 13 units
2) Let the coordinates of B be (x, y)
Using mid-point formula, we have
`-2 = (3+x)/2`
`-4 = 3 + x`
x = -7
`5 = (7 + y)/2`
`10 = -7 + y`
y = 17
Thus, the coordinates of points B are (-7, 17).
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