How to find the endpoints of a line segment - GRE Quantitative Reasoning

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Question

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

Answer

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:

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Question

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

Answer

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:

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Question

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

Answer

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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Question

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

Answer

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

Compare your answer with the correct one above

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