GRE Math : Midpoint Formula

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Example Questions

Example Question #1 : How To Find The Endpoints Of A Line Segment

There is a line defined by two end-points, (4,3) and (a,b) . The midpoint between these two points is (7,15) . What is the value of the point (a,b) ?

Possible Answers:

(14,-1)

(3,12)

(12,3)

(13,41)

(10,27)

Correct answer:

(10,27)

Explanation:

Recall that to find the midpoint of two points (a,b) and (c,d) , you use the equation:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$ .

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

So, for our equation, we know the following:

$\left(\frac{4+a}{2},\frac{3+b}{2}\right)=(7,15)$

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

$\frac{4+a}{2}=7$

4+a=14

a=10

Then, for the y-coordinate:

$\frac{3+b}{2}=15$

3+b=30

b=27

Therefore, our other point is: (10,27)

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Example Question #2 : How To Find The Endpoints Of A Line Segment

There is a line defined by two end-points, (11,-5) and (a,b) . The midpoint between these two points is (-6,-21) . What is the value of the point (a,b) ?

Possible Answers:

(12,-14)

(-23,-37)

(5,-26)

(4,-194)

(-14,-25)

Correct answer:

(-23,-37)

Explanation:

Recall that to find the midpoint of two points (a,b) and (c,d) , you use the equation:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$ .

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

So, for our equation, we know the following:

$\left(\frac{11+a}{2},\frac{-5+b}{2}\right)=(-6,-21)$

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

$\frac{11+a}{2}=-6$

11+a=-12

a=-23

Then, for the y-coordinate:

$\frac{-5+b}{2}=-21$

-5+b=-42

b=-37

Therefore, our other point is: (-23,-37)

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Example Question #3 : How To Find The Endpoints Of A Line Segment

What is the other endpoint of a line segment with one point that is (6,8) and a midpoint of (14,1) ?

Possible Answers:

(22,8)

(12,7)

(-15,-6)

(7,16)

(22,-6)

Correct answer:

(22,-6)

Explanation:

Recall that the midpoint formula is like finding the average of the and values for two points. For two points (a,b) and (c,d) , it is:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$

For our points, we are looking for (c,d) . We know:

$\left(\frac{6+c}{2},\frac{8+d}{2}\right)=(14,1)$

We can solve for each of these coordinates separately:

X-Coordinate

$\frac{6+c}{2} = 14$

6+c=28

c=22

Y-Coordinate:

$\frac{8+d}{2}=1$

8+d=2

d=-6

Therefore, our point is (22,-6)

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Example Question #1 : How To Find The Endpoints Of A Line Segment

What is the other endpoint of a line segment with one point that is (-15,14) and a midpoint of (-19,4) ?

Possible Answers:

(-12,-9)

(-23,-6)

(-14,-14)

(-20,-12)

(14,17)

Correct answer:

(-23,-6)

Explanation:

What is the other endpoint of a line segment with one point that is (-15,14) and a midpoint of (-19,4) ?

Recall that the midpoint formula is like finding the average of the and values for two points. For two points (a,b) and (c,d) , it is:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$

For our points, we are looking for (c,d) . We know:

$\left(\frac{-15+c}{2},\frac{14+d}{2}\right)=(-19,4)$

We can solve for each of these coordinates separately:

X-Coordinate

$\frac{-15+c}{2}=-19$

-15+c=-38

c=-23

Y-Coordinate:

$\frac{14+d}{2}=4$

14+d=8

d=-6

Therefore, our point is (-23,-6)

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Example Question #1 : Midpoint Formula

What is the midpoint of (2, 5) and (14, 18)?

Possible Answers:

(7, 9)

(16, 23)

(–10, –13)

(1, 2.5)

(8, 11.5)

Correct answer:

(8, 11.5)

Explanation:

The midpoint between two given points is found by solving for the average of each of the correlative coordinates of the given points. That is:

Midpoint = ( (2 + 14)/2 , (18 + 5)/2) = (16/2, 23/2) = (8, 11.5)

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Example Question #2 : How To Find The Midpoint Of A Line Segment

What is the midpoint between the points (1,3,7) and (–3,1,3)?

Possible Answers:

(3,1,2)

(2,–1,5)

(2,2,5)

(–1,2,5)

(5,2,4)

Correct answer:

(–1,2,5)

Explanation:

To find the midpoint, we add up the corresponding coordinates and divide by 2.

[1 + –3] / 2 = –1

[3 + 1] / 2 = 2

[7 + 3] / 2 = 5

Then the midpoint is (–1,2,5).

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Example Question #71 : Coordinate Geometry

A line which cuts another line segment into two equal parts is called a ___________.

Possible Answers:

parallel line

transversal

horizontal line

midpoint

bisector

Correct answer:

bisector

Explanation:

This is the definition of a bisector.

A midpoint is the point on a line that divides it into two equal parts. The bisector cuts the line at the midpoint, but the midpoint is not a line.

A transversal is a line that cuts across two or more lines that are usually parallel.

Parallel line and horizontal line don't make sense as answer choices here. The answer is bisector.

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GRE Math : Midpoint Formula

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Find The Endpoints Of A Line Segment

Example Question #2 : How To Find The Endpoints Of A Line Segment

Example Question #3 : How To Find The Endpoints Of A Line Segment

Example Question #1 : How To Find The Endpoints Of A Line Segment

Example Question #1 : Midpoint Formula

Example Question #2 : How To Find The Midpoint Of A Line Segment

Example Question #71 : Coordinate Geometry

All GRE Math Resources

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