Question

A circle's diameter has endpoints at

Answer 1

Part (a)

We'll use the distance formula.

$(x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956$

The diameter is exactly $\sqrt{106}$ units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.

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Part (b)

We divide the diameter in half to get the radius.

Therefore, the radius is exactly $\frac{\sqrt{106}}{2}$ units long which is approximately 5.1478 units.