Question

The points (-5,2) and (4,4) are the endpoints of the diameter of a ˚le. Find the length of the radius of the ˚le?

a) 5.0
b) 6.5
c) 7.0
d) 7.5

Answer 1

The length of the radius of the circle is approximately 4.91.

Step-by-step explanation:

To find the length of the radius of the circle, we first need to find the distance between the two endpoints (-5,2) and (4,4) which is the diameter of the circle. We can use the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values, we get:

d = sqrt((4 - -5)^2 + (4 - 2)^2) = sqrt(9^2 + 2^2) = sqrt(81 + 4) = sqrt(85)

Since the diameter is twice the length of the radius, we can divide the distance by 2 to find the radius:

radius = sqrt(85) / 2 ≈ 4.91

Therefore, the length of the radius of the circle is approximately 4.91.