The diameter of a circle has endpoints P(–10, –2) and Q(4, 6).
b.Find the radius. If your answer is not an integer, express it in radical form.
To find the radius of the circle, we first need to find the midpoint of the diameter line segment PQ.
Midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Midpoint = ((-10 + 4)/2, (-2 + 6)/2)
Midpoint = (-6/2, 4/2)
Midpoint = (-3, 2)
Now, we can find the distance between one endpoint of the diameter and the midpoint to determine the radius.
Distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance = sqrt((4 - (-3))^2 + (6 - 2)^2)
Distance = sqrt((4 + 3)^2 + (6 - 2)^2)
Distance = sqrt(7^2 + 4^2)
Distance = sqrt(49 + 16)
Distance = sqrt(65)
Therefore, the radius of the circle is sqrt(65) or approximately 8.06.