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

Given π΄(β8, β3) and πΆ(4, 1), what are the coordinates of π΅ if πΆ is the midpoint of line segment π΄π΅?

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### Video Transcript

Given π΄ negative eight, negative three and πΆ four, one, what are the coordinates of π΅ if πΆ is the midpoint of line segment π΄π΅?

For some line segment π΄π΅, the midpoint is πΆ. This means the distance from point π΄ to point πΆ will be equal to the distance from point πΆ to point π΅. We know the coordinates of point π΄ and point πΆ. To find the coordinates of point π΅, weβll 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 πΆ is π₯, π¦. From there, we plug in our known values, and we can solve for point π΅ π₯ two, π¦ two. First, weβll 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.

Weβll 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 πΆ. The endpoint π΅ is located at the coordinate 16, five.