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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. - Mathematics

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.

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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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