### Video Transcript

Suppose π΄ is negative seven,
negative four; π΅ is six, negative nine; and π· is eight, negative two. If πΆ is the midpoint of both line
segment π΄π΅ and line segment π·πΈ, find point πΈ.

Letβs first sketch what we
know. We have a line segment π΄π΅ with
the midpoint πΆ. And πΆ is also the midpoint of line
segment π·πΈ. Weβre given the coordinates for π΄,
π΅, and π·. Our end goal is to find the
coordinates of point πΈ. But before we can find πΈ, weβll
need to know πΆ. Once we find πΆ, we can find
πΈ. And to do both of these things,
weβll need to remember that the midpoint formula looks like this.

The π₯-coordinate of the midpoint
is found by taking the π₯-coordinates from the endpoints and dividing by two. And the π¦-coordinate of the
midpoint is found by averaging the π¦-coordinates of the two endpoints. Since πΆ is the midpoint of π΄ and
π΅, weβll let π΄ be π₯ one, π¦ one and π΅ be π₯ two, π¦ two. The midpoint πΆ will be located at
negative seven plus six over two, negative four plus negative nine over two. Negative seven plus six over two is
negative one-half. And negative four plus negative
nine is negative 13. So, the π¦-coordinate is negative
13 over two. Now, we know where πΆ is
located. And weβre ready to think about
πΈ.

If πΆ is also the midpoint of π·πΈ,
then the coordinates of πΆ will be equal to the π₯-coordinates of π· and πΈ averaged
together and the π¦-coordinates of π· and πΈ averaged together. Weβre given the coordinates of
π·. Thatβs eight, negative two. And so, we plug that in. From here, weβll make two separate
equations. Weβll set negative one-half equal
to eight plus the π₯-coordinate of πΈ over two. And negative 13 over two is equal
to negative two plus the π¦-coordinate of πΈ over two. Weβll give ourselves a little bit
more room.

Since all of the denominators are
two, then the numerators are equal to each other. Negative one equals eight plus the
π₯-coordinate of πΈ. And to solve for that missing
value, we subtract eight from both sides. And we see the π₯-coordinate for
point πΈ is negative nine. To solve for the π¦-coordinate of
point πΈ, we add two to both sides. The π¦-coordinate of πΈ is negative
11. In coordinate form, point πΈ is
located at negative nine, negative 11.