P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
Answer Details
The radius of a circle is the distance from the center of the circle to any point on the circumference of the circle. In this question, we are given the two ends of the diameter of a circle, so the radius is half of the diameter.
The distance between two points (x1, y1) and (x2, y2) can be calculated using the Pythagorean theorem: √((x2 - x1)^2 + (y2 - y1)^2).
Applying this formula to points P and Q, we have:
√((6 - (-6))^2 + (6 - 1)^2) = √(12^2 + 5^2) = √(144 + 25) = √169 = 13.0
So, the diameter is 13.0 units, and the radius is half of that, which is 6.5 units.
Therefore, the answer is 6.5 units.