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

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #4 : Midpoint Formula

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

Possible Answers:

(7, 9)

(–10, –13)

(8, 11.5)

(1, 2.5)

(16, 23)

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)

Example Question #5 : Midpoint Formula

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

Possible Answers:

(–1,2,5)

(3,1,2)

(2,2,5)

(5,2,4)

(2,–1,5)

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).

Example Question #6 : Midpoint Formula

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

Possible Answers:

midpoint

bisector

parallel line

horizontal line

transversal

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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