Question

A circle's diameter has endpoints at

(-4,-7) and (5,-2).
a) What is the length of the diameter?
b) What is the length of the radius?

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 = √((x_1 - x_2)^2 + (y_1 - y_2)^2)\\\\d = √((-4-5)^2 + (-7-(-2))^2)\\\\d = √((-4-5)^2 + (-7+2)^2)\\\\d = √((-9)^2 + (-5)^2)\\\\d = √(81 + 25)\\\\d = √(106)\\\\d \approx 10.2956\\\\`

The diameter is exactly
`√(106)` units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.

========================================================

Part (b)

We divide the diameter in half to get the radius.

Therefore, the radius is exactly
`(√(106))/(2)` units long which is approximately 5.1478 units.