Question

Find the other endpoint of the line segment with the given endpoint and midpoint. Theendpoint is (9, -10) and the midpoint is (4, 8). What is the missing endpoint?

Answer 1

Explanation

We must find the other endpoint of a line with:

• midpoint M = (4, 8),

,

• first endpoint EP1 = (9, -10).

The parts of the line are given in the following graph:

So we see that the second endpoint is given by:

$EP2=M-U.$

The vector U is given by:

$U=EP1-M=(9,-10)-(4,8)=(9-4,-10-8)=(5,-18).$

Using this in the equation of the second endpoint, we get:

$EP2=(4,8)-(5,-18)=(4-5,8-(-18))=(-1,26).$Answer

The coordinates of the missing endpoint are (-1, 26).