Question

A segment in the complex plane has a midpoint at 3 – 2i. If one endpoint of the segment is at 7 i, what is the other endpoint? –1 – 5i 5 – 0. 5i 10 – i 11 4i.

Answer 1

The midpoint of a segment divides the segment into equal halves

The other endpoint is 1- 5i

How to determine the missing endpoint

The coordinates are given as:

Point 1: 7 + i

Midpoint: 3 - 2i

Represent the other endpoint with x.

So, we have:

2 * Midpoint = Point 1 + x

This gives

$2 * (3 - 2i) =7 + i + x$

$6 - 4i =7 + i + x$

Collect like terms

$x = 6 -7- 4i -i$

Evaluate the like terms

$x = 1- 5i$

Hence, the other endpoint is 1- 5i

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