GMAT Math : Calculating the midpoint of a line segment

Study concepts, example questions & explanations for GMAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Calculating The Midpoint Of A Line Segment

Which of the following quadrants can contain the midpoint of a line segment with endpoints  and  for some nonzero value of ?

Possible Answers:

Quadrants I and III

Quadrants II and III

Quadrants III and IV

Quadrants II and IV

Quadrants I and IV

Correct answer:

Quadrants II and IV

Explanation:

The midpoint of the line segment with endpoints  and   is , or 

If , then the -coordinate is negative and the -coordinate is positive, so the midpoint is in Quadrant II. If , the reverse is true, so the midpoint is in Quadrant IV.

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

The midpoint of a line segment with endpoints  and  is . Sove for .

Possible Answers:

It cannot be determined from the information given.

Correct answer:

It cannot be determined from the information given.

Explanation:

The midpoint of a line segment with endpoints  is 

.

Substitute the coordinates of the endpoints, then set each equation to the appropriate midpoint coordinate. 

-coordinate:  

-coordinate: 

 

Simplify each, then solve the system of linear equations in two variables:

 

 

 

The two linear equations turn out to be equivalent, meaning that there are infinitely many solutions to the system. Therefore, insufficient information is given to answer the question.

Example Question #3 : Calculating The Midpoint Of A Line Segment

Find the midpoint of the points  and .

Possible Answers:

Correct answer:

Explanation:

Add the corresponding points together and divide both values by 2:

(\frac{2+4}{2},\frac{9+3}{2}) = (3, 6)

Example Question #4 : Calculating The Midpoint Of A Line Segment

What is the midpoint of and ?

Possible Answers:

Correct answer:

Explanation:

Add the x-values and divide by 2, and then add the y-values and divide by 2.  Be careful of the negatives!

Example Question #5 : Calculating The Midpoint Of A Line Segment

Consider segment  which passes through the points  and .

What are the correct coordinates for the midpoint of ?

Possible Answers:

Correct answer:

Explanation:

Midpoint formula is as follows:

Plug in and calculate:

Example Question #6 : Calculating The Midpoint Of A Line Segment

Segment  has endpoints of  and . If the midpoint of  is given by point , what are the coordinates of point ?

Possible Answers:

Correct answer:

Explanation:

Midpoints can be found using the following:

Plug in our points (-6,8) and (4,26) to find the midpoint.

Example Question #7 : Calculating The Midpoint Of A Line Segment

What are the coordinates of the mipdpoint of the line segment  if  and 

Possible Answers:

Correct answer:

Explanation:

The midpoint formula is 

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: