GRE Math : How to find the endpoints of a line segment

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #61 : Coordinate Geometry

There is a line defined by two end-points,  and .  The midpoint between these two points is .  What is the value of the point ?

Possible Answers:

Correct answer:

Explanation:

Recall that to find the midpoint of two points  and , you use the equation:

.

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

You merely need to solve each coordinate for its respective value.

Then, for the y-coordinate:

Therefore, our other point is: 

Example Question #1 : Midpoint Formula

There is a line defined by two end-points,  and .  The midpoint between these two points is .  What is the value of the point ?

Possible Answers:

Correct answer:

Explanation:

Recall that to find the midpoint of two points  and , you use the equation:

.

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

You merely need to solve each coordinate for its respective value.

Then, for the y-coordinate:

Therefore, our other point is: 

Example Question #2 : Midpoint Formula

What is the other endpoint of a line segment with one point that is  and a midpoint of ?

Possible Answers:

Correct answer:

Explanation:

Recall that the midpoint formula is like finding the average of the  and  values for two points.  For two points  and , it is:

For our points, we are looking for .  We know:

We can solve for each of these coordinates separately:

X-Coordinate

Y-Coordinate:

Therefore, our point is 

Example Question #3 : Midpoint Formula

What is the other endpoint of a line segment with one point that is  and a midpoint of ?

Possible Answers:

Correct answer:

Explanation:

What is the other endpoint of a line segment with one point that is  and a midpoint of ?

Recall that the midpoint formula is like finding the average of the  and  values for two points.  For two points  and , it is:

For our points, we are looking for .  We know:

We can solve for each of these coordinates separately:

X-Coordinate

Y-Coordinate:

Therefore, our point is 

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