GMAT Math : Calculating whether lines are perpendicular

Study concepts, example questions & explanations for GMAT Math

Create An Account Create Tests & Flashcards

All GMAT Math Resources

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

Example Questions

← Previous 1 2 Next →

Example Question #1 :Calculating Whether Lines Are Perpendicular

Find the equation of the line that is perpendicular to the line connecting the points $\dpi{100} \small (0,-4)\ and\ (-1,-7)$ ．

Possible Answers:

$\dpi{100} \small y=3x-1$

the line between points $\dpi{100} \small (0,0)\ and\ (2,2)$

$\dpi{100} \small y=-4x+8$

the line between the points $\dpi{100} \small (3,0)\ and\ (-3,2)$

$\dpi{100} \small y=\frac{x}{3}+1$

Correct answer:

the line between the points $\dpi{100} \small (3,0)\ and\ (-3,2)$

Explanation:

Lines are perpendicular if their slopes are negative reciprocals of each other. First we need to find the slope of the line in the question stem.

$slope = \frac{rise}{run} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{-7 + 4}{-1 - 0} = \frac{-3}{-1} = 3$

The negative reciprocal of 3 is $\dpi{100} \small -\frac{1}{3}$ , so our answer will have a slope of $\dpi{100} \small -\frac{1}{3}$ ．Let's go through the answer choices and see.

$\dpi{100} \small y=3x-1$ : This line is of the form $\dpi{100} \small y=mx+b$ , where $\dpi{100} \small m$ is the slope. The slope is 3, so this line is parallel, not perpendicular, to our line in question.

$\dpi{100} \small y=-4x+8$ : The slope here is $\dpi{100} \small -4$ , also wrong.

$\dpi{100} \small y=\frac{x}{3}+1$ : The slope of this line is $\dpi{100} \small \frac{1}{3}$ ．This is the reciprocal, but not the negative reciprocal, so this is also incorrect.

The line between the points $\dpi{100} \small (3,0)\ and\ (-3,2)$ : $\dpi{100} \small slope = \frac{2}{(-3-3)}=\frac{2}{-6}=-\frac{1}{3}$ ．

This is the correct answer! Let's check the last answer choice as well.

The line between points $\dpi{100} \small (0,0)\ and\ (2,2)$ : $\dpi{100} \small slope = \frac{2}{2}=1$ , which is incorrect.

Report an Error

Example Question #2 :Calculating Whether Lines Are Perpendicular

Determine whether the lines with equations 3y+x=2 and 4y-2x=3 are perpendicular.

Possible Answers:

There is not enough information to determine the answer

They are perpendicular

They are not perpendicular

Correct answer:

They are not perpendicular

Explanation:

If two equations are perpendicular, then they will have inverse negative slopes of each other. So if we compare the slopes of the two equations, then we can find the answer. For the first equation we have $3y+x=2\Rightarrow y=\frac{-1}{3}x+\frac{2}{3}$

so the slope is $-\frac{1}{3}$ ．

So for the equations to be perpendicular, the other equation needs to have a slope of 3. For the second equation, we have

$4y-2x=3\Rightarrow y=\frac{1}{2}x+\frac{3}{4}$

so the slope is $\frac{1}{2}$ ．

Since the slope of the second equation is not equal to 3, then the lines are not perpendicular.

Report an Error

Example Question #3 :Calculating Whether Lines Are Perpendicular

Transversal

Refer to the above figure. l || m ．True or false: $m \perp t$

Statement 1: $\angle 3 \cong \angle 5$

Statement 2: $\angle 2$ and $\angle 6$ are supplementary.

Possible Answers:

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If transversalcrosses two parallel linesand, then same-side interior angles are supplementary, so $\angle 3$ and $\angle 5$ are supplementary angles. Also, corresponding angles are congruent, so $\angle 2 \cong \angle 6$ ．

By Statement 1 alone, angles $\angle 3$ and $\angle 5$ are congruent as well as supplementary; by Statement 2 alone, $\angle 2$ and $\angle 6$ are also supplementary as well as congruent. Two angles that are both supplementary and congruent are both right angles, so from either statement alone,andintersect at right angles, so, consequently, $m \perp t$ ．

Report an Error

Example Question #4 :Calculating Whether Lines Are Perpendicular

Transversal

Figure NOT drawn to scale.

Refer to the above figure.

True or false: $m \perp t$

Statement 1: $\angle 4$ is a right angle.

Statement 2: $\angle 3$ and $\angle 5$ are supplementary.

Possible Answers:

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 alone establishes by definition that $l\perp t$ , but does not establish any relationship betweenand．

By Statement 2 alone, since same-side interior angles are supplementary, l || m ,但没有结论可以得出关系nship of, since the actual measures of the angles are not given.

Assume both statements are true. If two lines are parallel, then any line in their plane perpendicular to one must be perpendicular to the other. l || m and $l\perp t$ , so it can be established that $m \perp t$ ．

Report an Error

Example Question #5 :Calculating Whether Lines Are Perpendicular

Find the equation of the line that is perpendicular to the following equation and passes through the point (4,7) ．

$y=-\frac{x}{2}+14$

Possible Answers:

y=2x-1

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

y=4x-8

y=2x+1

y=2x-14

Correct answer:

y=2x-1

Explanation:

To solve this equation, we want to begin by recalling how to find the slope of a perpendicular line. In this case, our original line is modeled by the following:

$y=-\frac{x}{2}+14$

To find the slope of any line perpendicular to the above equation, we simply need to take the reciprocal of the first slope, and then change its sign. Our original slope is $-\frac{1}{2}$ , so

$m=-\frac{1}{2}$

becomes

{m}'=2 ．

If we flip $\frac{1}{2}$ , we get, and the opposite sign of a negative is a positive; hence, our slope is positive．

So, we know our perpendicular line should look something like this:

y=2x+b

However, we need to find out what(our-intercept) is in order to complete our equation. To do so, we need to plug in the ordered pair we received in the question, (4,7) , and solve for:

7=2*4+b

7=8+b

7-8=b

b=-1

So, by putting everything together, we get our final equation:

y=2x-1

This equation satisfies the conditions of being perpendicular to our initial equation and passing through (4,7) ．

Report an Error

Example Question #6 :Calculating Whether Lines Are Perpendicular

Which of the following lines is perpendicular to $y=-\frac{3}{4}x+7$ ?

Possible Answers:

方程的两个垂直于给予n line.

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

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

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

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

Correct answer:

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

Explanation:

In order for a lineto be perpendicular to another linedefined by the equation y=mx+b , the slope of linemust be a negative reciprocal of the slope of line．Since line's slope isin the slope-intercept equation above, line's slope would therefore be $-\frac{1}{m}$ ．

In this instance, $m=-\frac{3}{4}$ , so $-\frac{1}{m}=-\frac{1}{-\frac{3}{4}}=\frac{4}{3}$ ．Therefore, the correct solution is $y=\frac{4}{3}x+7$ ．

Report an Error

Example Question #7 :Calculating Whether Lines Are Perpendicular

A given linehas a slope of m=6 ．是什么slope of any line perpendicular to?

Possible Answers:

Not enough information provided

$-\frac{1}{6}$

Correct answer:

$-\frac{1}{6}$

Explanation:

Given that we have a linewith a slope m=6 , we can therefore conclude that any perpendicular line would have a slope $-\frac{1}{m}=-\frac{1}{6}$ ．

Report an Error

Example Question #8 :Calculating Whether Lines Are Perpendicular

Which of the following lines are perpendicular to $y=\frac{5}{6}x+10$ ?

Possible Answers:

$y=-\frac{6}{5}x-7$

$y=-\frac{6}{5}x+10$

$y=-\frac{5}{6}x-2$

Two answers are perpendicular to the given line.

$y=\frac{5}{6}x-7$

Correct answer:

Two answers are perpendicular to the given line.

Explanation:

Since in this instance the slope $m=\frac{5}{6}$ , $-\frac{1}{m}=-\frac{1}{\frac{5}{6}}=-\frac{6}{5}$ ．Two of the above answers have this as their slope, so therefore that is the answer to our question.

Report an Error

Example Question #9 :Calculating Whether Lines Are Perpendicular

Do the functions f(x) and g(x) intersect at a ninety-degree angle, and how can you tell?

$\small f(x)=3x+7$

$\small g(x)=-\frac{1}{3}x+7$

Possible Answers:

Yes, because the slope of g(x) is the reciprocal of the slope of f(x) and it has the opposite sign.

No, because f(x) and g(x) never intersect.

It is impossible to determine from the information provided.

Yes, because f(x) and g(x) have the same y-intercept.

No, because f(x) and g(x) have different slopes.

Correct answer:

Yes, because the slope of g(x) is the reciprocal of the slope of f(x) and it has the opposite sign.

Explanation:

If two lines intersect at a ninety-degree angle, they are said to be perpendicular. Two lines are perpendicular if their slopes are opposite reciprocals. In this case:

$f(x)\:slope=\frac{3}{1}$

$g(x)\:slope=-\frac{1}{3}$

The two lines' slopes are reciprocals with opposing signs, so the answer is yes. Of our two yes answers, only one has the right explanation. Eliminate the option dealing with-intercepts.

Report an Error

Example Question #10 :Calculating Whether Lines Are Perpendicular

Find the slope of a line that is perpendicular to the line running through the points (7,4) and (5,8) ．

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Not enough information provided.

Correct answer:

$\frac{1}{2}$

Explanation:

To find the slopeof the line running through (7,4) and (5,8) , we use the following equation:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-4}{5-7}=\frac{4}{-2}=-2$

The slope of any line perpendicular to the given line would have a slope that is the negative reciprocal of, or $-\frac{1}{m}$ ．Therefore, $-\frac{1}{-2}=\frac{1}{2}$

Report an Error

← Previous 1 2 Next →

All GMAT Math Resources

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

Popular Subjects

Calculus Tutors in San Francisco-Bay Area,Math Tutors in Phoenix,Spanish Tutors in Seattle,SSAT Tutors in Denver,Physics Tutors in Atlanta,ACT Tutors in San Diego,LSAT Tutors in Dallas Fort Worth,English Tutors in Phoenix,Biology Tutors in Washington DC,Physics Tutors in New York City

Popular Courses & Classes

SSAT Courses & Classes in San Diego,MCAT Courses & Classes in Miami,SAT Courses & Classes in Atlanta,SSAT Courses & Classes in Houston,MCAT Courses & Classes in Chicago,Spanish Courses & Classes in Chicago,ISEE Courses & Classes in Denver,MCAT Courses & Classes in San Francisco-Bay Area,ACT Courses & Classes in Seattle,MCAT Courses & Classes in Denver

Popular Test Prep

MCAT Test Prep in Chicago,GMAT Test Prep in San Francisco-Bay Area,GRE Test Prep in Chicago,SSAT Test Prep in Chicago,LSAT Test Prep in Seattle,MCAT Test Prep in Houston,LSAT Test Prep in Phoenix,ISEE Test Prep in Chicago,SAT Test Prep in Denver,GMAT Test Prep in Phoenix

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
63105年密苏里州圣路易斯

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)

GMAT Math : Calculating whether lines are perpendicular

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 :Calculating Whether Lines Are Perpendicular

Example Question #2 :Calculating Whether Lines Are Perpendicular

Example Question #3 :Calculating Whether Lines Are Perpendicular

Example Question #4 :Calculating Whether Lines Are Perpendicular

Example Question #5 :Calculating Whether Lines Are Perpendicular

Example Question #6 :Calculating Whether Lines Are Perpendicular

Example Question #7 :Calculating Whether Lines Are Perpendicular

Example Question #8 :Calculating Whether Lines Are Perpendicular

Example Question #9 :Calculating Whether Lines Are Perpendicular

Example Question #10 :Calculating Whether Lines Are Perpendicular

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: