Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Points and Distance Formula

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Points And Distance Formula

Find the length of the line segment from the origin to the point (3, 4).

Possible Answers:

Correct answer:

Explanation:

Here, we need to use the distance formula between the two points (0, 0) and (3, 4).

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

$d=\sqrt{(3-0)^2+(4-0)^2}$

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

Report an Error

Example Question #2 : Points And Distance Formula

I have two points, (–8,3) and (6,–1). If I want to connect those two points with a line segment, how long would that line segment need to be?

Possible Answers:

Infinite

$\frac{5}{2}$

$2\sqrt{53}$

$8\sqrt{2}$

Correct answer:

$2\sqrt{53}$

Explanation:

To determine how long the line needs to be to connect those two points, we need to use the distance formula, shown below.

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

The two points are (x_1,y_1) and (x_2,y_2) . In our case, the points are (–8, 3) and (6, –1).

$d=\sqrt{(6-(-8))^2+(-1-3)^2}$

$d=\sqrt{14^2+(-4)^2}$

$d=\sqrt{196+14}$

$d=\sqrt{212}$

$d=\sqrt{4(53)}$

$d=2\sqrt{53}$

So in order to connect the two points, the length of the line needs to have $d=2\sqrt{53}$ .

Report an Error

Example Question #3 : How To Find The Length Of A Line With Distance Formula

What is the distance between the points (7,8) and (10,4) ?

Possible Answers:

$\sqrt{7}$

$\sqrt{20}$

Correct answer:

Explanation:

To solve problems like this, we simply need to use the distance formula, $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ . Plugging in the and values from our points yields $d = \sqrt{(10-7)^{2}+(4-8)^{2}}$ , or $d = \sqrt{(3)^{2}+(-4)^{2}}$ . Solving this radical gives us a value of $d = \sqrt{25}$ , or 5.

Report an Error

Example Question #3 : Points And Distance Formula

Find the length of the line segment with endpoints at (2,9) and (7,6) .

Possible Answers:

None of the other answers are correct.

Correct answer:

None of the other answers are correct.

Explanation:

Use the distance formula, with $x_{1} =2,x_{2} =7,y_{1} =9,y_{2} =6$ :

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

$= \sqrt{ \left (2 -7\right ) ^{2} + \left (9 -6 \right ) ^{2} }$

$= \sqrt{ \left (-5 \right ) ^{2} + 3 ^{2} } = \sqrt{34} \approx 5.8$

Therefore, none of the integer answer choices are correct.

Report an Error

Example Question #5 : How To Find The Length Of A Line With Distance Formula

Find the distance between the two points (-4,2) and (2,1) .

Possible Answers:

$\sqrt{37}$

$\sqrt{5}$

Correct answer:

$\sqrt{37}$

Explanation:

The distance between two points can be found with the equation $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . Substituting in values you get $\sqrt{(2+4)^2+(1-2)^2}$ . This means that the answer is $\sqrt{37}$ .

Report an Error

Example Question #6 : How To Find The Length Of A Line With Distance Formula

Find the distance between the midpoints of line A with the points (-3,4) and (3,4) and line. B with the points (-2,-2) and (2,2) .

Possible Answers:

$\frac{3}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

Use the midpoint formula:

$\frac{x_{2}+x_{1}}{2}, \frac{y_{2}+y_{1}}{2}$

Remember points are written in the following format:

(x,y)

Substitute for line A

$\frac{\left ( -3+3 \right )}{2} , \frac{\left ( 4+0 \right )}{2}$

$\frac{\left ( 0\right )}{2} , \frac{\left ( 4\right )}{2}$

The midpoint of line A is (0,4) .

Substitute for line B.

$\frac{\left ( -2+2 \right )}{2} , \frac{\left ( -2 +2 \right )}{2}$

$\frac{\left ( 0 \right )}{2} , \frac{\left ( 0 \right )}{2}$

The midpoint of line B is (0,0) .

Now we can find the distance between these two points using the distance formula:

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

Substitute the using the known values for lines A and B.

$d= \sqrt{\left ( 0-0 \right )^{2} + \left ( 0-4 \right )^{2}}$

Simplify.

$d= \sqrt{\left ( 0\right )^{2} + \left ( -4 \right )^{2}}$

$d= \sqrt{\left ( -4 )^{2}}$

$d= \sqrt{16}$

The distance between the two midpoints of lines A and B is .

Report an Error

Example Question #7 : How To Find The Length Of A Line With Distance Formula

Find the distance between the following points:

$(3,1), \: (-2,7)$

Possible Answers:

$\sqrt{65}$

$\left(\frac{1}{2},4\right)$

$\sqrt{29}$

$\sqrt{61}$

Correct answer:

$\sqrt{61}$

Explanation:

Use the equation to calculated the distance between two points:

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

where

$(3,1)=(x_1,y_1), \: (-2,7)=(x_2,y_2)$

we can find the distance.

$d=\sqrt{(-2-3)^{2}+(7-1)^{2}}$

$=\sqrt{25+36}$

$=\sqrt{61}$

Report an Error

Example Question #6 : How To Find The Length Of A Line With Distance Formula

$\small (12,20)(2,4)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {192}$

$\small \sqrt {456}$

$\small \sqrt {356}$

$\small \sqrt {35}$

Correct answer:

$\small \sqrt {356}$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates.

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small \small \small d=\small \sqrt{(12-2)^{2}+(20-4)^{2}} \\ \\ = \sqrt{10^{2}+16^{2}}\\ \\ = \sqrt{100+256} \\ \\= \sqrt {356}$ .

This is the length.

Report an Error

Example Question #7 : How To Find The Length Of A Line With Distance Formula

$\small (4,6)(10,2)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {203}$

$\small \sqrt {62}$

$\sqrt {52}$

$\small \sqrt {19}$

Correct answer:

$\sqrt {52}$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (4,6)(10,2)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small \small \small \small d=\small \sqrt{(10-4)^{2}+(2-6)^{2}} \\ \\= \sqrt{6^{2}+(-4)^{2}} \\ \\= \sqrt{36+16} \\ \\= \sqrt {52}$ .

This is the length.

Report an Error

Example Question #4 : Points And Distance Formula

$\small (4,5)(6,7)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt 8$

$\small 18$

$\small 8$

$\small \sqrt {18}$

Correct answer:

$\small \sqrt 8$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (4,5)(6,7)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small \small \small \small \small d=\small \sqrt{(6-4)^{2}+(7-5)^{2}} \\ \\= \sqrt{2^{2}+2^{2}} \\ \\= \sqrt{4+4} \\ \\= \sqrt 8$ .

This is the length.

Report an Error

View Algebra Tutors

Arianna
Certified Tutor

Washington State University, Bachelor in Arts, Communication, General. City University of Seattle, Masters in Business Admini...

View Algebra Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Algebra Tutors

Ivory
Certified Tutor

Hopkinsville Community College, Associate, Associates in Science. Western Kentucky University, Bachelor in Arts, Psychology.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SSAT Tutors in Phoenix, Computer Science Tutors in Boston, Math Tutors in Miami, SAT Tutors in San Francisco-Bay Area, Math Tutors in Chicago, SAT Tutors in Los Angeles, LSAT Tutors in Phoenix, Biology Tutors in Los Angeles, Reading Tutors in Boston, Statistics Tutors in San Diego

Popular Courses & Classes

MCAT Courses & Classes in Denver, SSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in New York City, MCAT Courses & Classes in New York City, MCAT Courses & Classes in Phoenix, LSAT Courses & Classes in New York City, ACT Courses & Classes in Seattle, LSAT Courses & Classes in Miami, SSAT Courses & Classes in New York City, Spanish Courses & Classes in Los Angeles

Popular Test Prep

ACT Test Prep in Los Angeles, SSAT Test Prep in Washington DC, ISEE Test Prep in San Diego, SSAT Test Prep in New York City, MCAT Test Prep in Dallas Fort Worth, GRE Test Prep in San Diego, ACT Test Prep in Seattle, LSAT Test Prep in Los Angeles, MCAT Test Prep in Boston, ACT Test Prep in Atlanta

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

Algebra 1 : Points and Distance Formula

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : Points And Distance Formula

Example Question #2 : Points And Distance Formula

Example Question #3 : How To Find The Length Of A Line With Distance Formula

Example Question #3 : Points And Distance Formula

Example Question #5 : How To Find The Length Of A Line With Distance Formula

Example Question #6 : How To Find The Length Of A Line With Distance Formula

Example Question #7 : How To Find The Length Of A Line With Distance Formula

Example Question #6 : How To Find The Length Of A Line With Distance Formula

Example Question #7 : How To Find The Length Of A Line With Distance Formula

Example Question #4 : Points And Distance Formula

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: