GMAT Math : Midpoint Formula

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #11 : Coordinate Geometry

A line segment has its midpoint at  and an endpoint at .  What are the coordinates of the other endpoint?

Possible Answers:

Correct answer:

Explanation:

Because we are given the midpoint and one of the endpoints, we know the x coordinate of the other endpoint will be the same distance away from the midpoint in the x direction, and the y coordinate of the other endpoint will be the same distance away from the midpoint in the y direction. Given two endpoints of the form:

The midpoint of these two endpoints has the coordinates:

Plugging in values for the given midpoint and one of the endpoints, which we can see is  because it lies to the right of the midpoint, we can solve for the other endpoint as follows:

So the other endpoint has the coordinates  

Example Question #2 : Calculating The Endpoints Of A Line Segment

Consider segment  with endpoint  at . If the midpoint of  can be found at , what are the coordinates of point ?

 

Possible Answers:

Correct answer:

Explanation:

Recall midpoint formula:

In this case we have (x'y') and one of our other (x,y) points.

Plug and chug:

If you make this into two equations and solve you get the following.

 

 

 

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