A circle has a diameter with endpoints at –3 + 18i and 7 – 6i. Which point is also on the circle?

The center of the circle is the midpoint of the diameter’s endpoints: (−3 + 18i + 7 − 6i)/2 = 2 + 6i. The distance from this center to either endpoint is 13, so a point on the circle must be 13 units from 2 + 6i. For 14 + 11i, the difference is 12 + 5i, whose magnitude is √(12² + 5²) = 13. Therefore, 14 + 11i is on the circle.

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