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