Video Transcript
Given π΄ negative eight, negative
three and πΆ four, one, what are the coordinates of π΅ if πΆ is the midpoint of line
segment π΄π΅?
For some line segment π΄π΅, the
midpoint is πΆ. This means the distance from point
π΄ to point πΆ will be equal to the distance from point πΆ to point π΅. We know the coordinates of point π΄
and point πΆ. To find the coordinates of point
π΅, weβll consider the midpoint formula. For a midpoint π₯, π¦, the
π₯-coordinate will be equal to the average of the π₯-coordinates of the two
endpoints. We can write that as π₯ one plus π₯
two divided by two. And the π¦-coordinate of the
midpoint will be equal to the average of the π¦-coordinates of the two endpoints,
written here as π¦ one plus π¦ two divided by two.
We let π΄ be π₯ one, π¦ one and π΅
equal to π₯ two, π¦ two, then our midpoint πΆ is π₯, π¦. From there, we plug in our known
values, and we can solve for point π΅ π₯ two, π¦ two. First, weβll find the π₯-coordinate
of our point π΅ by setting four equal to negative eight plus π₯ two over two. Multiplying both sides of the
equation by two gives us eight is equal to negative eight plus π₯ two. From there, we add eight to both
sides of the equation, which gives us 16 is equal to π₯ two. The π₯-coordinate of point π΅ must
be 16.
Weβll follow the same process to
find the π¦-coordinate. We set one equal to negative three
plus π¦ two over two, multiply through by two gives us two equals negative three
plus π¦ two. And adding three to both sides
gives us π¦ two equal to five. The π¦-coordinate of point π΅ is
then equal to five. The line segment π΄π΅ has endpoints
π΄ and π΅ and a midpoint of πΆ. The endpoint π΅ is located at the
coordinate 16, five.