GMAT Math : Perpendicular Lines

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 #1 : Calculating The Equation Of A Perpendicular Line

What is the equation of the line that is perpendicular to y=2x+10 and goes through point (5,1) ?

Possible Answers:

$y=-\frac{1}{2}x+\frac{7}{2}$

$y=2x+\frac{7}{2}$

$y=-2x+\frac{7}{2}$

$y=\frac{1}{2}x+\frac{7}{2}$

Correct answer:

$y=-\frac{1}{2}x+\frac{7}{2}$

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.

The slope for the given line is , from y=2x+10 (y=mx+b) , where is the slope. Therefore, the negative reciprocal is $-\frac{1}{2}$ .

$m=-\frac{1}{2}$ and (5,1) :

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

$y-1=-\frac{1}{2}(x-5)$

$y-1=-\frac{1}{2}x+\frac{5}{2}$

$y=-\frac{1}{2}x+\frac{5}{2}+1$

$y=-\frac{1}{2}x+\frac{5}{2}+\frac{2}{2}$

$y=-\frac{1}{2}x+\frac{7}{2}$

Report an Error

Example Question #2 : Calculating The Equation Of A Perpendicular Line

Write the equation of a line that is perpendicular to $y=\frac{-1}{2}x+4$ and goes through point (0,6) ?

Possible Answers:

$y=\frac{-1}{2}x+6$

$y=\frac{1}{2}x+6$

y=2x+6

y=-2x+6

Correct answer:

y=2x+6

Explanation:

A perpendicular line has a negative reciprocal slope to the given line.

The given line, $y=\frac{-1}{2}x+4$ , has a slope of $-\frac{1}{2}$ , as is the slope in the standard form equation (y=mx+b) .

Slope of perpendicular line: m=2

Point: (0,6)

Using the point slope formula, we can solve for the equation:

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

y-6=2(x-0)

y-6=2x

y=2x+6

Report an Error

Example Question #1 : Calculating The Equation Of A Perpendicular Line

Given h(x) , find the equation of a line that is perpendicular to h(x) and goes through the point (14,0) .

$\small h(x)=-\frac{5}3x-12$

Possible Answers:

$\small \small y=-\frac{3x}{5}-\frac{42}{5}$

$\small \small y=\frac{3x}{5}+\frac{5}{42}$

$\small \small y=\frac{3x}{5}+\frac{42}{5}$

$\small \small y=-\frac{5x}{3}-\frac{42}{5}$

$\small y=\frac{3x}{5}-\frac{42}{5}$

Correct answer:

$\small y=\frac{3x}{5}-\frac{42}{5}$

Explanation:

Given

$\small h(x)=-\frac{5}3x-12$

We need a perpendicular line going through (14,0).

Perpendicular lines have opposite reciprocal slopes.

So we get our slope to be

$\small \frac{3}{5}$

Next, plug in all our knowns into y=mx+b and solve for .

$0=14\cdot \frac{3}{5}+b$

$\small b=-\frac{42}{5}$ .

Making our answer

$\small y=\frac{3x}{5}-\frac{42}{5}$ .

Report an Error

Example Question #892 : Problem Solving Questions

Given the function f(x)=4x+9 , which of the following is the equation of a line perpendicular to f(x) and has a -intercept of ?

Possible Answers:

$g(x)=\frac{1}{4}x-7$

$g(x)=-\frac{1}{4}x+7$

g(x)=4x+9

$g(x)=-\frac{1}{4}x-7$

$g(x)=\frac{1}{4}x+7$

Correct answer:

$g(x)=-\frac{1}{4}x+7$

Explanation:

Given a line defined by the equation f(x)=mx+b with slope , any line that is perpendicular to must have a slope $-\frac{1}{m}$ , or the negative reciprocal of .

Since f(x)=4x+9 , the slope is and the slope of any line g(x) parallel to f(x) must have a slope of $-\frac{1}{m}=-\frac{1}{4}$ .

Since g(x) also needs to have a -intercept of , then the equation for g(x) must be $g(x)=-\frac{1}{4}x+7$ .

Report an Error

Example Question #893 : Problem Solving Questions

Given the function f(x)=-5x-4 , which of the following is the equation of a line perpendicular to f(x) and has a -intercept of ?

Possible Answers:

$g(x)=\frac{1}{5}x-8$

$g(x)=\frac{1}{5}x+8$

g(x)=5x+8

$g(x)=-\frac{1}{5}x-8$

$g(x)=-\frac{1}{5}x+8$

Correct answer:

$g(x)=\frac{1}{5}x+8$

Explanation:

Given a line defined by the equation f(x)=mx+b with slope , any line that is perpendicular to must have a slope $-\frac{1}{m}$ , or the negative reciprocal of .

Since f(x)=-5x-4 , the slope is and the slope of any line g(x) parallel to f(x) must have a slope of $-\frac{1}{m}=-\frac{1}{-5}=\frac{1}{5}$ .

Since g(x) also needs to have a -intercept of , then the equation for g(x) must be $g(x)=\frac{1}{5}x+8$ .

Report an Error

Example Question #894 : Problem Solving Questions

Given the function f(x)=7x+2 , which of the following is the equation of a line perpendicular to f(x) and has a -intercept of ?

Possible Answers:

$g(x)=\frac{1}{7}x+9$

None of the above

$g(x)=-\frac{1}{7}x+9$

$g(x)=\frac{1}{7}x-9$

$g(x)=-\frac{1}{7}x-9$

Correct answer:

$g(x)=-\frac{1}{7}x-9$

Explanation:

Given a line defined by the equation f(x)=mx+b with slope , any line that is perpendicular to must have a slope $-\frac{1}{m}$ , or the negative reciprocal of .

Since f(x)=7x+2 , the slope is and the slope of any line g(x) parallel to f(x) must have a slope of $-\frac{1}{m}=-\frac{1}{7}$ .

Since g(x) also needs to have a -intercept of , then the equation for g(x) must be $g(x)=-\frac{1}{7}x-9$ .

Report an Error

Example Question #895 : Problem Solving Questions

Determine the equation of a line perpendicular to y=3x-2 at the point (2,4) .

Possible Answers:

$y=-\frac{1}{3}x-\frac{10}{3}$

$y=-\frac{1}{3}x+\frac{14}{3}$

$y=\frac{1}{3}x+\frac{4}{3}$

$y=\frac{1}{3}x+4$

$y=-\frac{1}{3}x+\frac{7}{3}$

Correct answer:

$y=-\frac{1}{3}x+\frac{14}{3}$

Explanation:

The equation of a line in standard form is written as follows:

y=mx+b

Where is the slope of the line and is the y intercept. First, we can determine the slope of the perpendicular line using the knowledge that its slope must be the negative reciprocal of the slope of the line to which it is perpendicular. For the given line, we can see that m=3 , so the slope of a line perpendicular to it will be the negative reciprocal of that value, which gives us:

$m_{perp}=-\frac{1}{m}=-\frac{1}{3}$

Now that we know the slope of the perpendicular line, we can plug its value into the formula for a line along with the coordinates of the given point, allowing us to calculate the -intercept, :

$4=-\frac{1}{3}(2)+b$

$b=\frac{14}{3}$

We now have the slope and the -intercept of the perpendicular line, which is all we need to write its equation in standard form:

$y=-\frac{1}{3}x+\frac{14}{3}$

Report an Error

Example Question #1 : Calculating The Slope Of A Perpendicular Line

What is the slope of the line perpendicular to -9x-9y=9 ?

Possible Answers:

m=9

$m=-\frac{1}{9}$

m=-1

m=1

Correct answer:

m=1

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, rewrite the equation in slope intercept form (y=mx+b) :

-9x-9y=9

-9y=9x+9

y=-x-1

Slope of given line:

Negative reciprocal: m=1

Report an Error

Example Question #1 : Calculating The Slope Of A Perpendicular Line

Line 1 is the line of the equation x + y = 17 . Line 2 is perpendicular to this line. What is the slope of Line 2?

Possible Answers:

$- \frac{1}{17}$

Correct answer:

Explanation:

Rewrite in slope-intercept form:

x + y = 17

x + y -x = 17-x

y = -x + 17

y = -1x + 17

The slope of the line is the coefficient of , which is . A line perpendicular to this has as its slope the opposite of the reciprocal of :

$m = -\frac{1}{-1} = 1$

Report an Error

Example Question #1 : Calculating The Slope Of A Perpendicular Line

Given:

$\small f(x)=\frac{5}{6}x-17$

Calculate the slope of g(x) , a line perpendicular to f(x) .

Possible Answers:

$\small 5$

$\small -\frac{5}{6}$

$\small \frac{6}{5}$

$\small -6$

$\small -\frac{6}{5}$

Correct answer:

$\small -\frac{6}{5}$

Explanation:

To find the slope of a line perpendicular to a given line, simply take the opposite reciprocal of the slope of the given line.

Since f(x) is given in slope intercept form,

$y=mx+b \rightarrow m=slope$ .

Therefore our original slope is

$m=\small \frac{5}{6}$

So our new slope becomes:

$m_{new}=-\frac{1}{m}=-\frac{1}{\frac{5}{6}}=\small -\frac{6}{5}$

Report an Error

All GMAT Math Resources

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

Popular Subjects

SAT Tutors in Boston, Algebra Tutors in Boston, LSAT Tutors in Chicago, GMAT Tutors in Washington DC, English Tutors in Seattle, LSAT Tutors in San Francisco-Bay Area, Math Tutors in Dallas Fort Worth, English Tutors in San Francisco-Bay Area, Chemistry Tutors in Philadelphia, French Tutors in San Diego

Popular Courses & Classes

LSAT Courses & Classes in Denver, GRE Courses & Classes in Philadelphia, GMAT Courses & Classes in Philadelphia, GRE Courses & Classes in Boston, ISEE Courses & Classes in Philadelphia, SAT Courses & Classes in Phoenix, GMAT Courses & Classes in Seattle, SAT Courses & Classes in Miami, SAT Courses & Classes in Denver, SSAT Courses & Classes in Houston

Popular Test Prep

ISEE Test Prep in Houston, GMAT Test Prep in Los Angeles, LSAT Test Prep in New York City, GRE Test Prep in Dallas Fort Worth, SAT Test Prep in San Diego, LSAT Test Prep in Atlanta, GRE Test Prep in Denver, ISEE Test Prep in Philadelphia, MCAT Test Prep in San Diego, ISEE Test Prep in Chicago

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 : Perpendicular Lines

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Equation Of A Perpendicular Line

Example Question #2 : Calculating The Equation Of A Perpendicular Line

Example Question #1 : Calculating The Equation Of A Perpendicular Line

Example Question #892 : Problem Solving Questions

Example Question #893 : Problem Solving Questions

Example Question #894 : Problem Solving Questions

Example Question #895 : Problem Solving Questions

Example Question #1 : Calculating The Slope Of A Perpendicular Line

Example Question #1 : Calculating The Slope Of A Perpendicular Line

Example Question #1 : Calculating The Slope Of A Perpendicular Line

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details