Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Distance Formula

Study concepts, example questions & explanations for Intermediate Geometry

Create An Account

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #11 : Distance Formula

Find the length of y = -2x + 3 for the interval $-10 \leq y \leq 15$ .

Possible Answers:

13.463

22.355

25.005

9.657

27.951

Correct answer:

27.951

Explanation:

First, we need to figure out the x-coordinates of the endpoints so that we can use the distance formula, $\sqrt{(x_1 - x_2 )^2 + (y_1 - y_2 ) ^ 2 }$

Plug in -10 for y and solve for x:

-10 = -2x + 3 subtract 3 from both sides

-13 = -2x divide both sides by -2

6.5 = x

Plug in 15 for y and solve for x:

15 = -2x + 3 subtract 3 from both sides

12 = -2x divide both sides by -2

-6 = x

The endpoints are (6.5, -10) and (-6, 15 ) . We could choose either point to be (x_1, y_1) . Let's choose (6.5, -10 ) .

$\sqrt{(6.5 -- 6 )^2 + (-10 - 15 )^2 }= \sqrt { 12.5^2 + (-25)^2 } = \sqrt{156.25 + 625}= \sqrt{781.25} \approx 27.951$

Report an Error

Example Question #12 : Distance Formula

Find the length of the line 2x - 4 y + 10 = 0 for the interval $-5 \leq x \leq 0$ .

Possible Answers:

7.500

4.330

5.590

2.500

15.811

Correct answer:

5.590

Explanation:

To calculate the distance, first find the y-coordinates of the endpoints by plugging the x-coordinates into the equation.

First plug in -5

2(-5) - 4y + 10 = 0

-10 -4y + 10 = 0 combining like terms, we get -10 + 10 is 0

-4 y = 0 divide by -4

y = 0

Now plug in 0

2(0 ) - 4 y + 10 = 0

-4y + 10 = 0 subtract 10 from both sides

-4y = -10 divide by -4

y = 2.5

The endpoints are (-5, 0 ) and (0, 2.5) , and now we can plug these points into the distance formula:

$\sqrt{(-5 - 0 )^2 + (0 - 2.5)^2 } = \sqrt{(-5)^2 + (-2.5)^2 } = \sqrt{25 + 6.25} \approx 5.590$

Report an Error

Example Question #13 : Distance Formula

Find the length of $y = \frac{1}{4}x + 3$ on the interval $- 8 \leq x \leq 12$ .

Possible Answers:

20.616

8.602

21.190

6.403

8.062

Correct answer:

20.616

Explanation:

To find the length, we need to first find the y-coordinates of the endpoints.

First, plug in -8 for x:

$y = \frac{1}{4} (-8) + 3 = -2 + 3 = 1$

Now plug in 12 for x:

$y = \frac{1}{4} (12 ) + 3 = 3 + 3 = 6$

Our endpoints are (-8, 1) and (12, 6 ) .

To find the length, plug these points into the distance formula:

$\sqrt{(6-1)^2 + (12--8)^2 } = \sqrt{5^2 + 20^2 } = \sqrt{25 + 400 } \approx 20.616$

Report an Error

Example Question #14 : Distance Formula

Jose is walking from his house to the grocery store. He walks 120 feet north, then turns left to walk another 50 feet west. On the way back home, Jose finds a straight line shortcut back to his house. How long is this shortcut?

Possible Answers:

$150\ ft.$

$130\ ft.$

$170\ ft.$

$90\ ft.$

Correct answer:

$130\ ft.$

Explanation:

When walking north and then taking a left west, a 90 degree angle is formed. When Jose returns home going in a straight line, this will now form the hypotenuse of a right triangle. The legs of the triangle are 120 ft and 50 ft respectively.

To solve, use the pythagorean formula.

$50^{2}+120^{2}=c^{2}$

$2500+14400=c^{2}$

$16900=c^{2}$

$\sqrt{16900}=\sqrt{c^{2}}$

130=c

130 ft is the straight line distance home.

The distance formula could also be used to solve this problem.

We will assume that home is at the point (0,0)

$Distance=\sqrt{(50-0)^{2}+(120-0)^{2}}$

Distance = 130 ft.

Report an Error

Example Question #11 : How To Find The Length Of A Line With Distance Formula

A line has endpoints at (8,4) and (5,10). How long is this line?

Possible Answers:

$5\sqrt{3}$

$\sqrt{5}$

None of these.

$3\sqrt{5}$

Correct answer:

$3\sqrt{5}$

Explanation:

We find the exact length of lines using their endpoints and the distance formula.

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

Given the endpoints,

(x_1,y_1)=(8,4)

(x_2,y_2)=(5, 10)

the distance formula becomes,

$\sqrt{(5-8)^2+(10-4)^2}=\sqrt{9+36}=\sqrt{45}=\sqrt{9\cdot 5}=\mathbf{3\sqrt{5}}$ .

Report an Error

Example Question #71 : Lines

Find the length of a line with endpoints at (10, 2) and (5, -6) .

Possible Answers:

$\sqrt{89}$

$\sqrt{91}$

$\sqrt{85}$

$\sqrt{87}$

Correct answer:

$\sqrt{89}$

Explanation:

Recall the distance formula for a line with two endpoints $(x_1, y_1)\text{ and }(x_2, y_2)$ :

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

Plug in the given points to find the length of the line:

$\text{distance}=\sqrt{(5-10)^2+(-6-2)^2}=\sqrt{89}$

Report an Error

Example Question #17 : Distance Formula

A line segment on the coordinate plane has its endpoints at (3.8, -1.7) and (9.2, 5.5) .

Give the length of the segment to the nearest whole tenth.

Possible Answers:

6.6

15.2

13.5

9.0

14.8

Correct answer:

9.0

Explanation:

The distance between endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ on the coordinate plane can be calculated using the distance formula

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

Set $x_{1}= 3.8, y_{1} =-1.7,x_{2} =9.2, y_{2}= 5.5$ , and evaluate:

$d = \sqrt{(9.2-3.8)^{2}+[5.5 -(-1.7)]^{2}}$

$= \sqrt{5.4 ^{2}+7.2^{2}}$

$= \sqrt{29.16+51.84}$

$= \sqrt{81}$

= 9 ,

the correct length.

Report an Error

← Previous 1 2 Next →

View Tutors

Aida M
Certified Tutor

Universidad Del Valle, Bachelor in Arts, Education.

View Tutors

Jazimine
Certified Tutor

The University of Texas System Office, Bachelor of Science, Accounting.

View Tutors

Shimila
Certified Tutor

University of Colorado Boulder, Bachelor of Science, Sociology. University of Denver, Master of Arts, Legal Administrative As...

All Intermediate Geometry Resources

8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Denver, SAT Tutors in Washington DC, SSAT Tutors in Miami, Reading Tutors in New York City, Spanish Tutors in San Francisco-Bay Area, GRE Tutors in Seattle, Physics Tutors in Los Angeles, MCAT Tutors in Boston, Calculus Tutors in New York City, Calculus Tutors in Seattle

Popular Courses & Classes

ISEE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in San Diego, SAT Courses & Classes in San Diego, MCAT Courses & Classes in Houston, ISEE Courses & Classes in Seattle, SAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Los Angeles, Spanish Courses & Classes in Chicago, GRE Courses & Classes in New York City, GRE Courses & Classes in Houston

Popular Test Prep

SSAT Test Prep in Houston, SSAT Test Prep in Washington DC, GRE Test Prep in Philadelphia, LSAT Test Prep in Houston, GMAT Test Prep in Atlanta, ISEE Test Prep in New York City, SAT Test Prep in Miami, SSAT Test Prep in Miami, GMAT Test Prep in Washington DC, GRE 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
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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Intermediate Geometry : Distance Formula

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #11 : Distance Formula

Example Question #12 : Distance Formula

Example Question #13 : Distance Formula

Example Question #14 : Distance Formula

Example Question #11 : How To Find The Length Of A Line With Distance Formula

Example Question #71 : Lines

Example Question #17 : Distance Formula

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: