GMAT Math : Geometry

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 #2 : Other Lines

Solve for $\displaystyle x$ in the coordinate (x,1) $\displaystyle (x,1)$ on line 3y=4x+1 $\displaystyle 3y=4x+1$?

Possible Answers:

$\displaystyle -1$

$\displaystyle 1$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 2$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

To solve for $\displaystyle x$ for y=1 $\displaystyle y=1$, we have to plug 1 into the $\displaystyle y$ variable of the equation and solve for $\displaystyle x$:

3y=4x+1 $\displaystyle 3y=4x+1$

$\displaystyle 3(1)=4x+1$

3=4x+1 $\displaystyle 3=4x+1$

3-1=4x $\displaystyle 3-1=4x$

2=4x $\displaystyle 2=4x$

$x=\frac{1}{2}$ $\displaystyle x=\frac{1}{2}$

Report an Error

Example Question #3 : Calculating Whether Point Is On A Line With An Equation

Solve for $\displaystyle y$ in the coordinate (5,y) $\displaystyle (5,y)$ on line $\displaystyle 14y-10x=20$?

Possible Answers:

$\displaystyle 70$

$\displaystyle 5$

$\displaystyle -5$

$\displaystyle -70$

Correct answer:

$\displaystyle 5$

Explanation:

To solve for $\displaystyle y$ for x=5 $\displaystyle x=5$, we have to plug $\displaystyle 5$ into the $\displaystyle x$ variable of the equation and solve for $\displaystyle y$:

$\displaystyle 14y-10x=20$

$\displaystyle 14y-10(5)=20$

$\displaystyle 14y-50=20$

$\displaystyle 14y=20+50$

14y=70 $\displaystyle 14y=70$

$\displaystyle y=5$

Report an Error

Example Question #1 : Calculating Whether Point Is On A Line With An Equation

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

If the point $\left ( 16,y\right )$ $\displaystyle \left ( 16,y\right )$ is on $\overline{JK}$ $\displaystyle \overline{JK}$, what is the value of y?

Possible Answers:

$\displaystyle -5$

$\displaystyle 5$

$\displaystyle 11$

$\displaystyle 0$

$\displaystyle -11$

Correct answer:

$\displaystyle 11$

Explanation:

First, use the points to find the equation of JK:

Given that JK passes through (4,5) and (144,75) we can find the slope as follows:

Slope is found via:

$m=\frac{y'-y}{x'-x}$ $\displaystyle m=\frac{y'-y}{x'-x}$

Plug in and calculate:

$\small \small m=\frac{75-5}{144-4}=\frac{70}{140}=\frac{1}{2}$ $\displaystyle \small \small m=\frac{75-5}{144-4}=\frac{70}{140}=\frac{1}{2}$

Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).

$\small 5=\frac{1}{2}*4+b$ $\displaystyle \small 5=\frac{1}{2}*4+b$

$\small b=5-2=3$ $\displaystyle \small b=5-2=3$

So our answer is:

$\small y=\frac{x}{2}+3$ $\displaystyle \small y=\frac{x}{2}+3$

To find y, we need to plug in 16 for x and solve:

$\small \small y=\frac{16}{2}+3=8+3=11$ $\displaystyle \small \small y=\frac{16}{2}+3=8+3=11$

Report an Error

Example Question #4 : Calculating Whether Point Is On A Line With An Equation

If f(x) $\displaystyle f(x)$ is defined as follows, is the point $\left ( -2,5\right )$ $\displaystyle \left ( -2,5\right )$on f(x) $\displaystyle f(x)$?

$\small f(x)=4x+13$ $\displaystyle \small f(x)=4x+13$

Possible Answers:

Yes

Cannot be calculated from the provided information

f(x) is undefined at (-2,5)

Correct answer:

Yes

Explanation:

To find out if (-2,5) is on f(x), simply plug the point into f(x)

$\small f(x)=4x+13$ $\displaystyle \small f(x)=4x+13$

Becomes,

$\small \small 5=4*-2+13=-8+13=5$ $\displaystyle \small \small 5=4*-2+13=-8+13=5$

So yes, it does!

Report an Error

Example Question #5 : Calculating Whether Point Is On A Line With An Equation

Which of the following are points along g(x) $\displaystyle g(x)$ if

${}g(x)=4x^2-8$ $\displaystyle {}g(x)=4x^2-8$.

Possible Answers:

(3,28) $\displaystyle (3,28)$

$\displaystyle (-3,-28)$

(4,64) $\displaystyle (4,64)$

(3,-28) $\displaystyle (3,-28)$

(2,4) $\displaystyle (2,4)$

Correct answer:

(3,28) $\displaystyle (3,28)$

Explanation:

One way to solve this one is by plugging in each of the answer choices and eliminating any that don't work out. Begin with our original g(x)

${}g(x)=4x^2-8$ $\displaystyle {}g(x)=4x^2-8$

If we plug in 3 we get

${}g(x)=4(3)^2-8=4(9)-8=36-8=28$ $\displaystyle {}g(x)=4(3)^2-8=4(9)-8=36-8=28$,

So our point is (3,28).

Report an Error

Example Question #1 : Calculating The Equation Of A Line

What is the equation of a line with slope $\displaystyle 1$ and a point (1,4) $\displaystyle (1,4)$?

Possible Answers:

y=x+4 $\displaystyle y=x+4$

y=x+3 $\displaystyle y=x+3$

y=x-4 $\displaystyle y=x-4$

y=x+1 $\displaystyle y=x+1$

Correct answer:

y=x+3 $\displaystyle y=x+3$

Explanation:

Since the slope and a point on the line are given, we can use the point-slope formula:

$y-y_{1}=m(x-x_{1})$ $\displaystyle y-y_{1}=m(x-x_{1})$

$m=1\ and\ (1,4)$ $\displaystyle m=1\ and\ (1,4)$

$\displaystyle y-4=1(x-1)$

y-4=x-1 $\displaystyle y-4=x-1$

y=x-1+4 $\displaystyle y=x-1+4$

$\displaystyle y=x+3$

Report an Error

Example Question #2 : Calculating The Equation Of A Line

What is the equation of a line with slope $\displaystyle 0$ and point (5,2) $\displaystyle (5,2)$?

Possible Answers:

y=x+2 $\displaystyle y=x+2$

y=x+5 $\displaystyle y=x+5$

y=2 $\displaystyle y=2$

y=5 $\displaystyle y=5$

Correct answer:

y=2 $\displaystyle y=2$

Explanation:

Since the slope and a point on the line are given, we can use the point-slope formula:

$y-y_{1}=m(x-x_{1})$ $\displaystyle y-y_{1}=m(x-x_{1})$

$m=0\ and\ (5,2)$ $\displaystyle m=0\ and\ (5,2)$

$\displaystyle y-2=0(x-5)$

y-2=0 $\displaystyle y-2=0$

$\displaystyle y=2$

Report an Error

Example Question #3 : Calculating The Equation Of A Line

What is the equation of a line with slope $-\frac{4}{3}$ $\displaystyle -\frac{4}{3}$ and a point (-8,7) $\displaystyle (-8,7)$?

Possible Answers:

$y=-\frac{4}{3}x-\frac{3}{11}$ $\displaystyle y=-\frac{4}{3}x-\frac{3}{11}$

$y=\frac{4}{3}x+\frac{11}{3}$ $\displaystyle y=\frac{4}{3}x+\frac{11}{3}$

$y=-\frac{4}{3}x-\frac{11}{3}$ $\displaystyle y=-\frac{4}{3}x-\frac{11}{3}$

$y=\frac{4}{3}x+\frac{32}{3}$ $\displaystyle y=\frac{4}{3}x+\frac{32}{3}$

Correct answer:

$y=-\frac{4}{3}x-\frac{11}{3}$ $\displaystyle y=-\frac{4}{3}x-\frac{11}{3}$

Explanation:

Since the slope and a point on the line are given, we can use the point-slope formula:

$y-y_{1}=m(x-x_{1})$ $\displaystyle y-y_{1}=m(x-x_{1})$

slope: $-\frac{4}{3}$ $\displaystyle -\frac{4}{3}$ and point: (-8,7) $\displaystyle (-8,7)$

$y-7=-\frac{4}{3}(x-(-8))$ $\displaystyle y-7=-\frac{4}{3}(x-(-8))$

$y-7=-\frac{4}{3}(x+8)$ $\displaystyle y-7=-\frac{4}{3}(x+8)$

$y-7=-\frac{4}{3}x-\frac{32}{3}$ $\displaystyle y-7=-\frac{4}{3}x-\frac{32}{3}$

$y=-\frac{4}{3}x-\frac{32}{3}+7$ $\displaystyle y=-\frac{4}{3}x-\frac{32}{3}+7$

$y=-\frac{4}{3}x-\frac{32}{3}+\frac{21}{3}$ $\displaystyle y=-\frac{4}{3}x-\frac{32}{3}+\frac{21}{3}$

$y=-\frac{4}{3}x-\frac{11}{3}$ $\displaystyle y=-\frac{4}{3}x-\frac{11}{3}$

Report an Error

Example Question #1 : Calculating The Equation Of A Line

Find the equation of the line through the points (4, -2) $\displaystyle (4, -2)$ and (1, 7) $\displaystyle (1, 7)$.

Possible Answers:

y=2x+9 $\displaystyle y=2x+9$

y=-3 $\displaystyle y=-3$

y=3x+3 $\displaystyle y=3x+3$

y=2x-2 $\displaystyle y=2x-2$

$\displaystyle y=-3x+10$

Correct answer:

$\displaystyle y=-3x+10$

Explanation:

First find the slope of the equation.

$m =\frac{rise}{run} =\frac{7 + 2}{1-4} = \frac{9}{-3}=-3$ $\displaystyle m =\frac{rise}{run} =\frac{7 + 2}{1-4} = \frac{9}{-3}=-3$

Now plug in one of the two points to form an equation. Here we use (4, -2), but either point will produce the same answer.

$y-(-2)=-3(x-4)$ $\displaystyle y-(-2)=-3(x-4)$

$y + 2=-3x + 12$ $\displaystyle y + 2=-3x + 12$

$y=-3x+10$ $\displaystyle y=-3x+10$

Report an Error

Example Question #1 : Calculating The Equation Of A Line

Find the equation of $\overline{JK}$ $\displaystyle \overline{JK}$ in the form y=mx+b $\displaystyle y=mx+b$.

Possible Answers:

$\small y=\frac{x}{2}+3$ $\displaystyle \small y=\frac{x}{2}+3$

$\small \small y=-\frac{x}{2}+3$ $\displaystyle \small \small y=-\frac{x}{2}+3$

$\small \small y=\frac{x}{2}+6$ $\displaystyle \small \small y=\frac{x}{2}+6$

$\small \small y=\frac{x}{2}-3$ $\displaystyle \small \small y=\frac{x}{2}-3$

$\small \small y=2x+3$ $\displaystyle \small \small y=2x+3$

Correct answer:

$\small y=\frac{x}{2}+3$ $\displaystyle \small y=\frac{x}{2}+3$

Explanation:

Given that JK passes through (4,5) and (144,75) we can find the slope as follows:

Slope is found via:

$m=\frac{y'-y}{x'-x}$ $\displaystyle m=\frac{y'-y}{x'-x}$

Plug in and calculate:

$\small \small m=\frac{75-5}{144-4}=\frac{70}{140}=\frac{1}{2}$ $\displaystyle \small \small m=\frac{75-5}{144-4}=\frac{70}{140}=\frac{1}{2}$

Next, we need to use one of our points and the slope to find our y-intercept. I'll use (4,5).

$\small 5=\frac{1}{2}*4+b$ $\displaystyle \small 5=\frac{1}{2}*4+b$

$\small b=5-2=3$ $\displaystyle \small b=5-2=3$

So our answer is:

$\small y=\frac{x}{2}+3$ $\displaystyle \small y=\frac{x}{2}+3$

Report an Error

All GMAT Math Resources

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

Popular Subjects

MCAT Tutors in Miami, LSAT Tutors in Chicago, Chemistry Tutors in New York City, SAT Tutors in Washington DC, SSAT Tutors in Miami, Physics Tutors in Miami, GRE Tutors in Houston, ACT Tutors in Houston, Algebra Tutors in Phoenix, SSAT Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Houston, SAT Courses & Classes in Chicago, GMAT Courses & Classes in Miami, ACT Courses & Classes in Philadelphia, SSAT Courses & Classes in Atlanta, GRE Courses & Classes in Atlanta, Spanish Courses & Classes in Atlanta, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Boston

Popular Test Prep

ACT Test Prep in Houston, SAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Chicago, GMAT Test Prep in Denver, ISEE Test Prep in Los Angeles, SAT Test Prep in Los Angeles, LSAT Test Prep in San Diego, SAT Test Prep in Chicago, SSAT Test Prep in Atlanta, SAT Test Prep in Denver

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 : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Other Lines

Example Question #3 : Calculating Whether Point Is On A Line With An Equation

Example Question #1 : Calculating Whether Point Is On A Line With An Equation

Example Question #4 : Calculating Whether Point Is On A Line With An Equation

Example Question #5 : Calculating Whether Point Is On A Line With An Equation

Example Question #1 : Calculating The Equation Of A Line

Example Question #2 : Calculating The Equation Of A Line

Example Question #3 : Calculating The Equation Of A Line

Example Question #1 : Calculating The Equation Of A Line

Example Question #1 : Calculating The Equation Of A Line

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details