GMAT Math : Calculating the endpoints of a line segment

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

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

Example Questions

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

Example Question #11 : Coordinate Geometry

A line segment has its midpoint at (-1,3) and an endpoint at (3,8) . What are the coordinates of the other endpoint?

Possible Answers:

(-3,-8)

(-2,-5)

(-5,-2)

(-3,-1)

(-2,1)

Correct answer:

(-5,-2)

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:

(x_1,y_1),(x_2,y_2)

The midpoint of these two endpoints has the coordinates:

$(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Plugging in values for the given midpoint and one of the endpoints, which we can see is (x_2,y_2) because it lies to the right of the midpoint, we can solve for the other endpoint as follows:

$(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$(-1,3)=(\frac{x_1+3}{2},\frac{y_1+8}{2})$

$\frac{x_1+3}{2}=-1\rightarrow x_1+3=-2\rightarrow x_1=-5$

$\frac{y_1+8}{2}=3\rightarrow y_1+8=6\rightarrow y_1=-2$

So the other endpoint has the coordinates (-5,-2)

Report an Error

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

Consider segment with endpoint at (8,9) . If the midpoint of can be found at (-15, -67) , what are the coordinates of point ?

Possible Answers:

(38,143)

(-38,-143)

(-46,-150)

(143,38)

(-143,-38)

Correct answer:

(-38,-143)

Explanation:

Recall midpoint formula:

$(x',y')=\left(\frac{x^1+x^2}{2}, \frac{y^1+y^2}{2}\right)$

In this case we have (x'y') and one of our other (x,y) points.

Plug and chug:

$(-15,-67)=\left(\frac{8+x}{2}, \frac{9+y}{2}\right)$

If you make this into two equations and solve you get the following.

$\small -15=\frac{8+x}{2}, x=-38$

$\small -67=\frac{9+y}{2}, y=-143$

Report an Error

All GMAT Math Resources

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

Popular Subjects

Computer Science Tutors in Denver, Chemistry Tutors in Philadelphia, SSAT Tutors in Washington DC, GRE Tutors in Washington DC, English Tutors in Miami, Biology Tutors in Miami, GRE Tutors in Phoenix, English Tutors in Los Angeles, Spanish Tutors in Miami, SSAT Tutors in New York City

Popular Courses & Classes

MCAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Boston, ACT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Houston, LSAT Courses & Classes in San Diego, SSAT Courses & Classes in Washington DC, MCAT Courses & Classes in San Diego, GMAT Courses & Classes in Los Angeles, GMAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in San Diego

Popular Test Prep

SSAT Test Prep in Philadelphia, SAT Test Prep in Chicago, GMAT Test Prep in Los Angeles, SSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Philadelphia, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Denver, SAT Test Prep in Boston, SSAT Test Prep in Washington DC, SAT Test Prep in Washington DC

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 : Calculating the endpoints of a line segment

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #4 : Midpoint Formula

Example Question #3 : Coordinate Geometry

Example Question #6 : Midpoint Formula

Example Question #11 : Coordinate Geometry

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

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details