GMAT Math : Lines

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #1 : Midpoint Formula

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

Possible Answers:

Quadrants II and III

Quadrants I and IV

Quadrants II and IV

Quadrants I and III

Quadrants III 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 : Midpoint Formula

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 : Midpoint Formula

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 #1 : Lines

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 : Midpoint Formula

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 : Midpoint Formula

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 : Midpoint Formula

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

Possible Answers:

Correct answer:

Explanation:

The midpoint formula is 

Example Question #8 : 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 #9 : Midpoint Formula

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 #10 : 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

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