# 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.

#### 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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