Question Video: Finding the Coordinates of a Point Using the Midpoint Formula Mathematics • 11th Grade

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.