A segment in the complex plane has a midpoint at –1 + i. If the segment has an endpoint at –5 – 7i, what is the other endpoint?

Let the other endpoint be z. The midpoint formula gives (−5 − 7i + z)/2 = −1 + i, so z = 2(−1 + i) − (−5 − 7i) = −2 + 2i + 5 + 7i = 3 + 9i. The other endpoint is 3 + 9i, choice D.

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