GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Coordinate Geometry

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 #841 : Gmat Quantitative Reasoning

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 #842 : Gmat Quantitative Reasoning

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 #4 : Coordinate Geometry

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 #4 : Coordinate Geometry

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 #5 : 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 

Example Question #3 : Midpoint Formula

The quadrilateral with vertices  is a trapezoid. What are the endpoints of its midsegment?

Possible Answers:

Correct answer:

Explanation:

The midsegment of a trapezoid is the segment whose endpoints are the midpoints of its legs - its nonparallel opposite sides. These two sides are the ones with endpoints  and . The midpoint of each can be found by taking the means of the - and -coordinates:

The midsegment is the segment that has endpoints (2,2) and (19,2)

Example Question #843 : Gmat Quantitative Reasoning

The midpoint of a line segment with endpoints  and  is . What is ?

Possible Answers:

It cannot be determined from the information given.

Correct answer:

Explanation:

If the midpoint of a line segment with endpoints  and  is , then by the midpoint formula, 

 

and

 .

The first equation can be simplified as follows:

 

or 

The second can be simplified as follows:

or 

This is a system of linear equations.  can be calculated by subtracting:

Example Question #5 : Midpoint Formula

If the midpoint of  is  and  is at , what are the coordinates of ?

Possible Answers:

Correct answer:

Explanation:

Midpoint formula is as follows:

In this case, we have x,y and the value of the midpoint. We need to findx' and y'

V is at (2,9) and the midpoint is at (6,7)

                       and                               

                         

 

So we have (10,5) as point U

Example Question #11 : Coordinate Geometry

A line segment has its midpoint at  and an endpoint at .  What are the coordinates of the other endpoint?

Possible Answers:

Correct answer:

Explanation:

Because we are given the midpoint and one of the endpoints, we know the x coordinate of the other endpoint will be the same distance away from the midpoint in the x direction, and the y coordinate of the other endpoint will be the same distance away from the midpoint in the y direction. Given two endpoints of the form:

The midpoint of these two endpoints has the coordinates:

Plugging in values for the given midpoint and one of the endpoints, which we can see is  because it lies to the right of the midpoint, we can solve for the other endpoint as follows:

So the other endpoint has the coordinates  

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