GMAT Math : Calculating the length of a line with distance 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 : Calculating The Length Of A Line With Distance Formula

A line segement on the coordinate plane has endpoints (A,B+3) and (A + 4, B) . Which of the following expressions is equal to the length of the segment?

Possible Answers:

$\sqrt{(2A+4)^{2} + (2B+3)^{2}}$

$\sqrt{7}$

$\sqrt{(2A-4)^{2} + (2B-3)^{2}}$

$\sqrt{(A-4)^{2} + (B-3)^{2}}$

Correct answer:

Explanation:

Apply the distance formula, setting

$x_{ 1} = A + 4, x_{2} = A ,y_{ 1} = B, y_{2} = B+3$ :

$d = \sqrt{(x_{2}- x_{1})^{2}+(y_{2}-y_{1})^{2}}$

$d = \sqrt{[A-(A+4)]^{2}+[(B+3)-B)]^{2}}$

$d = \sqrt{(-4)^{2}+3^{2}} = \sqrt{16+9} = \sqrt{25} = 5$

Report an Error

Example Question #1 : Distance Formula

What is distance between (6,7) and (1,5) ?

Possible Answers:

$\sqrt{29}$

$\sqrt{12}$

$\sqrt{7}$

$\sqrt{20}$

Correct answer:

$\sqrt{29}$

Explanation:

$distance= \sqrt{(x_{2}-x_{1})^2+y_{2}-y_{1})^2}$

$= \sqrt{(6-1)^2+(7-5)^2}$

$= \sqrt{(5)^2+(2)^2}$

$= \sqrt{(25+4)}$

$\sqrt{29}$

Report an Error

Example Question #2 : Distance Formula

What is the distance between the points (2, 5) and (7, 17) ?

Possible Answers:

$2\sqrt{5}$

Correct answer:

Explanation:

Let's plug our coordinates into the distance formula.

$\sqrt{(2-7)^{2}+(5-17)^{2}}= \sqrt{(-5)^{2}+(-12)^{2}} = \sqrt{25+144}= \sqrt{169} = 13$

Report an Error

Example Question #3 : Distance Formula

What is the distance between the points (1,4) and (5,2) ?

Possible Answers:

$2\sqrt{5}$

$3\sqrt{3}$

Correct answer:

$2\sqrt{5}$

Explanation:

We need to use the distance formula to calculate the distance between these two points.

$\sqrt{(1-5)^{2}+(4-2)^{2}} = \sqrt{(-4)^{2}+(2)^{2}} =\sqrt{20}=\sqrt{4}\sqrt{5}=2\sqrt{5}$

Report an Error

Example Question #5 : Calculating The Length Of A Line With Distance Formula

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

Find the length of segment $\overline{JK}$ .

Possible Answers:

$176.5\ \textup{units}$

$169.4\ \textup{units}$

$156.5\ \textup{units}$

$134.6\ \textup{units}$

$168.2\ \textup{units}$

Correct answer:

$156.5\ \textup{units}$

Explanation:

This question requires careful application of distance formula, which is really a modified form of Pythagorean theorem.

$\small d=\sqrt{(x-x')^2+(y-y')^2}$

Plug in everthing and solve:

$\small \small d=\sqrt{(144-4)^2+(75-7)^2}=\sqrt{24500}\approx156.5$

So our answer is 156.6

Report an Error

Example Question #6 : Calculating The Length Of A Line With Distance Formula

What is the length of a line segment that starts at the point (1,-3) and ends at the point (4,1) ?

Possible Answers:

Correct answer:

Explanation:

Using the distance formula for the length of a line between two points, we can plug in the given values and determine the length of the line segment by calculating the distance between the two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$d=\sqrt{(4-1)^2+(1-(-3))^2}$

$d=\sqrt{(3)^2+(4)^2}$

$d=\sqrt{25}$

d=5

Report an Error

All GMAT Math Resources

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

Popular Subjects

GMAT Tutors in Los Angeles, English Tutors in Houston, Math Tutors in San Diego, English Tutors in San Diego, Math Tutors in Philadelphia, French Tutors in Chicago, GMAT Tutors in Chicago, ACT Tutors in Miami, MCAT Tutors in San Diego, ISEE Tutors in Seattle

Popular Courses & Classes

ISEE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Miami, GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Washington DC, SAT Courses & Classes in Philadelphia, GRE Courses & Classes in Boston, GRE Courses & Classes in Phoenix, ISEE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Chicago, LSAT Courses & Classes in Philadelphia

Popular Test Prep

LSAT Test Prep in Denver, MCAT Test Prep in Denver, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in San Diego, SAT Test Prep in San Diego, SAT Test Prep in New York City, ACT Test Prep in Los Angeles, MCAT Test Prep in Boston, SSAT Test Prep in Atlanta, GMAT 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 length of a line with distance formula

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating The Length Of A Line With Distance Formula

Example Question #1 : Distance Formula

Example Question #2 : Distance Formula

Example Question #3 : Distance Formula

Example Question #5 : Calculating The Length Of A Line With Distance Formula

Example Question #6 : Calculating The Length Of A Line With Distance Formula

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details