Answer:
- center: (3, 2.5)
- radius: 8.5 units
Explanation:
The center of a circle is the midpoint of any diameter. The midpoint of a segment has coordinates that are the average of the coordinates of the segment end points.
The length of the radius is the distance from the center to an end point of a diameter. Alternatively, it is half the length of the diameter.
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Center = (A +B)/2 = ((7, -5) +(-1, 10))/2 = (6, 5)/2 = (3, 2.5)
Radius = 1/2|AB| = 1/2√((7 -(-1))² +(-5 -10)²) = 1/2√(64 +225) = 1/2√289
= 17/2 = 8.5
The center of the circle is (3, 2.5), and the radius is 8.5 units.
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Additional comment
The differences of diameter end point coordinates are 8 and 15, suggesting the Pythagorean triple {8, 15, 17} will come into play. It does.