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

Given 𝐴(βˆ’8, βˆ’3) and 𝐢(4, 1), what are the coordinates of 𝐡 if 𝐢 is the midpoint of line segment 𝐴𝐡?


Video Transcript

Given 𝐴 negative eight, negative three and 𝐢 four, one, what are the coordinates of 𝐡 if 𝐢 is the midpoint of line segment 𝐴𝐡?

For some line segment 𝐴𝐡, the midpoint is 𝐢. This means the distance from point 𝐴 to point 𝐢 will be equal to the distance from point 𝐢 to point 𝐡. We know the coordinates of point 𝐴 and point 𝐢. To find the coordinates of point 𝐡, we’ll consider the midpoint formula. For a midpoint π‘₯, 𝑦, 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 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 π‘₯ one, 𝑦 one and 𝐡 equal to π‘₯ two, 𝑦 two, then our midpoint 𝐢 is π‘₯, 𝑦. From there, we plug in our known values, and we can solve for point 𝐡 π‘₯ two, 𝑦 two. First, we’ll find the π‘₯-coordinate of our point 𝐡 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 𝐡 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 𝐡 is then equal to five. The line segment 𝐴𝐡 has endpoints 𝐴 and 𝐡 and a midpoint of 𝐢. The endpoint 𝐡 is located at the coordinate 16, five.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.