GMAT Math : Midpoint Formula

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Midpoint Formula

Which of the following quadrants can contain the midpoint of a line segment with endpoints (0,A) and (-A,0) for some nonzero value of ?

Possible Answers:

Quadrants III and IV

Quadrants II and III

Quadrants II and IV

Quadrants I and IV

Quadrants I and III

Correct answer:

Quadrants II and IV

Explanation:

The midpoint of the line segment with endpoints (0,A) and (-A,0) is $\left ( \frac{0+ (-A) }{2}, \frac{A+ 0 }{2}, \right )$ , or $\left (- \frac{A }{2}, \frac{A }{2}, \right )$

If A > 0 , then the -coordinate is negative and the -coordinate is positive, so the midpoint is in Quadrant II. If A < 0 , the reverse is true, so the midpoint is in Quadrant IV.

Report an Error

Example Question #1 : Coordinate Geometry

The midpoint of a line segment with endpoints (A + 2, 2B-1) and (B+4, 2A+1) is (8,10) . 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 $(x_{1}, y_{1}), (x_{2}, y_{2})$ is

$\left ( \frac{x_{1}+x_{2} }{2},\frac{y_{1}+y_{2} }{2} \right )$ .

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

-coordinate: $\frac{(A + 2)+ (B + 4) }{2} = 8$

-coordinate: $\frac{(2B-1)+(2A +1) }{2} = 10$

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

$\frac{(A + 2)+ (B + 4) }{2} = 8$

$\frac{(A + B + 6) }{2} = 8$

A + B + 6 = 16

A + B = 10

$\frac{(2B-1)+(2A +1) }{2} = 10$

$\frac{2A + 2B }{2} = 10$

A + B = 10

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.

Report an Error

Example Question #1 : Coordinate Geometry

Find the midpoint of the points (2, 9) and (4, 3) .

Possible Answers:

(6,12)

(3,6)

(2.5,5.5)

(-3,6)

(2,5)

Correct answer:

(3,6)

Explanation:

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

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

Report an Error

Example Question #2 : Coordinate Geometry

What is the midpoint of (-5,1) and (1,4) ?

Possible Answers:

$(2,\frac{5}{2})$

$(3,\frac{3}{2})$

(-3,6)

$(-2,\frac{5}{2})$

$(3,\frac{5}{2})$

Correct answer:

$(-2,\frac{5}{2})$

Explanation:

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

$(\frac{-5+1}{2},\frac{1+4}{2}) = (-2, \frac{5}{2})$

Report an Error

Example Question #4 : Coordinate Geometry

Consider segment $\overline{JK}$ which passes through the points $\left ( 4,5\right )$ and $\left ( 144,75\right )$ .

What are the correct coordinates for the midpoint of $\overline{JK}$ ?

Possible Answers:

$\small (74,40)$

$\small \small (74,35)$

$\small \small (75,45)$

$\small \small (73,42)$

$\small \small (70,35)$

Correct answer:

$\small (74,40)$

Explanation:

Midpoint formula is as follows:

$\small m=(\frac{x+x'}{2},\frac{y+y'}{2})$

Plug in and calculate:

$\small \small \small m=(\frac{4+144}{2},\frac{75+5}{2})=(74,40)$

Report an Error

Example Question #4 : Coordinate Geometry

Segment has endpoints of (-6,8) and (4,26) . If the midpoint of is given by point , what are the coordinates of point ?

Possible Answers:

(-1,17)

(17,-1)

(5,17)

(-5,-17)

(17,5)

Correct answer:

(-1,17)

Explanation:

Midpoints can be found using the following:

$midpoint(x,y)=\left(\frac{x+x'}{2},\frac{y+y'}{2}\right)$

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

$\small \small midpoint(x,y)=\left(\frac{-6+4}{2},\frac{8+26}{2}\right)=\left(\frac{-2}{2},\frac{34}{2}\right)=(-1,17)$

Report an Error

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

What are the coordinates of the mipdpoint of the line segment if A=(2,3) and B=(2,-7)?

Possible Answers:

(0,-2)

(2,4)

(2,-2)

(0,-10)

(0,4)

Correct answer:

(2,-2)

Explanation:

The midpoint formula is $(\frac{x_{2}+x_{1}}{2},\frac{y_{2}+y_{1}}{2}) = (\frac{2+2}{2},\frac{3+-7}{2})=(2,-2).$

Report an Error

Example Question #4 : Midpoint Formula

The quadrilateral with vertices (0,0),(22,0), (16,4), (4,4) is a trapezoid. What are the endpoints of its midsegment?

Possible Answers:

(0,0), (16,4)

(11,0),(10,4)

(2,2),(19,2 )

(0,2),(23,2 )

(22,0), (4,4)

Correct answer:

(2,2),(19,2 )

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 (0,0), (4,4) and (22,0), (16,4) . The midpoint of each can be found by taking the means of the - and -coordinates:

$(0,0), (4,4): \left ( \frac{0+4}{2},\frac{0+4}{2} \right ) \Rightarrow (2,2)$

$(22,0), (16,4): \left ( \frac{22+16}{2},\frac{0+4}{2} \right ) \Rightarrow (19,2)$

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

Report an Error

Example Question #3 : Coordinate Geometry

The midpoint of a line segment with endpoints (2A, B) and (B + 7, 3A - 2) is (9, 6) . What is ?

Possible Answers:

It cannot be determined from the information given.

Correct answer:

Explanation:

If the midpoint of a line segment with endpoints (2A, B) and (B + 7, 3A - 2) is (9, 6) , then by the midpoint formula,

$\frac{2A + (B + 7)}{2} = 9$

and

$\frac{B + (3A - 2)}{2} = 6$ .

The first equation can be simplified as follows:

2A + B + 7 = 18

2A + B = 11

The second can be simplified as follows:

3A + B - 2 = 12

3A + B = 14

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

3A + B = 14

$\underline{2A + B = 11 }$

$A \; \; \; \; \; \; \; \; = 3$

Report an Error

Example Question #6 : Midpoint Formula

If the midpoint of $\overline{VU}$ is $\left ( 6,7\right )$ and $\textup{Point }V$ is at $\left (2,9\right )$ , what are the coordinates of $\textup{Point }U$ ?

Possible Answers:

$\left ( -5,10\right )$

$\left ( 10,5\right )$

$\left ( 23,14\right )$

$\left ( 14,23\right )$

$\left ( 5,10\right )$

Correct answer:

$\left ( 10,5\right )$

Explanation:

Midpoint formula is as follows:

$\small \small m(x,y)=(\frac{x+x'}{2},\frac{y+y'}{2})$

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)

$\small 6=\frac{2+x'}{2}$ and $\small 7=\frac{9+y'}{2}$

$\small x'=6*2-2=10$ $\small y'=7*2-9=14-9=5$

So we have (10,5) as point U

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Washington DC, ACT Tutors in Seattle, ISEE Tutors in Denver, MCAT Tutors in Philadelphia, ISEE Tutors in Houston, French Tutors in Seattle, Math Tutors in Dallas Fort Worth, Biology Tutors in Houston, Spanish Tutors in Dallas Fort Worth, Spanish Tutors in Chicago

Popular Courses & Classes

MCAT Courses & Classes in Seattle, MCAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Atlanta, GMAT Courses & Classes in Chicago, SAT Courses & Classes in Atlanta, SSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Miami, SSAT Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Houston

Popular Test Prep

SSAT Test Prep in New York City, SAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Dallas Fort Worth, ACT Test Prep in Miami, SAT Test Prep in Phoenix, GRE Test Prep in Washington DC, SSAT Test Prep in Philadelphia, SAT Test Prep in Denver, SSAT Test Prep in Miami, SSAT Test Prep in San Francisco-Bay Area

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

Email address:
Your name:
Feedback:

GMAT Math : Midpoint Formula

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Midpoint Formula

Example Question #1 : Coordinate Geometry

Example Question #1 : Coordinate Geometry

Example Question #2 : Coordinate Geometry

Example Question #4 : Coordinate Geometry

Example Question #4 : Coordinate Geometry

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

Example Question #4 : Midpoint Formula

Example Question #3 : Coordinate Geometry

Example Question #6 : Midpoint Formula

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details