We are open Saturday and Sunday!

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

← Previous 1 2 3 4 5 6 7 8 9 Next →

Example Question #31 : Points And Distance Formula

Find the length of the line connecting the following two points. Simplify your answer.

(12,2) and (10,1)

Possible Answers:

$\sqrt{6}$

$\sqrt{3}$

$\sqrt{5}$

$2\sqrt{2}$

Correct answer:

$\sqrt{5}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(12,2) and (x_2,y_2)=(10,1)

$d=\sqrt{(12-10)^{2}+(2-1)^{2}}$

$d=\sqrt{2^{2}+1^{2}}$

$d=\sqrt{4+1}=\sqrt{5}$

Report an Error

Example Question #32 : Points And Distance Formula

Find the length of the connecting the following two points. Simplify your answer.

(-15,-5) and (-4,-1)

Possible Answers:

$\sqrt{136}$

$\sqrt{135}$

$\sqrt{134}$

$\sqrt{137}$

Correct answer:

$\sqrt{137}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(-15,-5) and (x_2,y_2)=(-4,-1)

$d=\sqrt{((-4)-(-15))^{2}+((-1)-(-5))^{2}}$

$d=\sqrt{11^{2}+4^{2}}$

$d=\sqrt{121+16}=\sqrt{137}$

Report an Error

Example Question #371 : Equations Of Lines

FInd the length of the line connecting the following two points. Simplify your answer.

(-12,16) and (-7,4)

Possible Answers:

$\sqrt{173}$

$\sqrt{171}$

Correct answer:

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(-7,4) and (x_2,y_2)=(-12,16)

$d=\sqrt{((-7)-(-12))^{2}+(4-16)^{2}}$

$d=\sqrt{5^{2}+(-12)^{2}}$

$d=\sqrt{25+144}=\sqrt{169}=13$

Report an Error

Example Question #34 : Points And Distance Formula

A line passes through the points (7,25) and (12,0) . What is the distance between these two points?

Possible Answers:

26.8

23.7

25.5

Correct answer:

25.5

Explanation:

The question is merely asking the distance between two points. This kind of problem can be quickly solved for by using the distance formula:

$d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ , where is distance and x_1 , x_2 , y_1 , and y_2 come from the given points.

This problem merely needs to have the and values substituted in for so we can solve for .

Arbitrarily assigning (x_1,y_1) and (x_2,y_2) , we substitute in our values as follows:

$d=\sqrt{(12-7)^2+(0-25)^2}$

$d=\sqrt{(5)^2+(-25)^2}$

$d=\sqrt{25+625}$

$d=\sqrt{650}$

$d=25.495 \approx {\color{Blue} 25.5}$

Report an Error

Example Question #35 : Points And Distance Formula

A line passes through (1,3) and (-9,32) . What's the distance between these two points?

Possible Answers:

31.4

30.7

30.6

27.9

33.6

Correct answer:

30.7

Explanation:

The question is merely asking the distance between two points. This kind of problem can be quickly solved for by using the distance formula:

$d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ , where is distance and x_1 , x_2 , y_1 , and y_2 come from the given points.

This problem merely needs to have the and values substituted in for so we can solve for .

Arbitrarily assigning (x_1,y_1) and (x_2,y_2) , we substitute in our values as follows:

$d=\sqrt{(1+9)^2+(3-32)^2}$

$d=\sqrt{(10)^2+(-29)^2}$

$d=\sqrt{100+841}$

$d=\sqrt{941}$

$d=30.6757 \approx {\color{Blue} 30.7}$

Report an Error

Example Question #36 : Points And Distance Formula

What is the distance between the following points?

Possible Answers:

33.6

17.4 36.1

23.5

52.3

Correct answer:

52.3

Explanation:

What is the distance between the following points?

To find distance, use distance formula:

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

Note, if you cannot recall distance formula think of Pythagorean theorem. When using distance formula, you are simply finding the length of the hypotenuse of a right triangle.

Anyway, start plugging in our points and simplify to the answer. We'll call our first point 1 and our second point 2

$d=\sqrt{(4--19)^2+(-6--53)^2}=\sqrt{(23)^2+(47)^2}=\sqrt{2738}\approx52.3$

So our answer is 52.3

Report an Error

Example Question #37 : Points And Distance Formula

What is the length of the distance between the points and ?

Possible Answers:

16.25

12.5

Correct answer:

Explanation:

What is the length of the distance between the points and ?

Find distance with distance formula, which is quite similar to Pythagorean Theorem

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

Now, let's call point 1 and point 2, then let's plug in and find d!

$d=\sqrt{(9-18)^2+(15-3)^2}=\sqrt{81+144}=\sqrt{225}=15$

So the distance is 15

Report an Error

Example Question #38 : Points And Distance Formula

Find the distance between the following points:

(14,25)(38,7)

Possible Answers:

Correct answer:

Explanation:

Find the distance between the following points:

(14,25)(38,7)

To find the distance between two points, use distance formula.

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

Distance formula is closely related to Pythagorean theorem. Pythagorean Theorem is:

a^2+b^2=c^2

Which can be rewritten as:

$c=\sqrt{a^2+b^2}$

Now, in distance formula, we are essentially finding the hypotenuse of a right triangle.

Anyway, to find the distance, we simply need to plug in the points we are given and simplify:

$d=\sqrt{(38-14)^2+(7-25)^2}=\sqrt{(24^2)+(-18)^2}$

Continue

$\sqrt{(24^2)+(-18)^2}=\sqrt{576+324}=\sqrt{900}=30$

So our hypotenuse (distance) is 30.

If you are really observant, you can see that the other two sides of the triangles are 24 and 18.

Report an Error

Example Question #39 : Points And Distance Formula

A line is connected by the points (1,3) and (4,2) . What is the distance of this line?

Possible Answers:

$\sqrt{10}$

$2\sqrt2$

$2\sqrt5$

$2\sqrt3$

Correct answer:

$\sqrt{10}$

Explanation:

Write the distance formula.

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

Substitute the values of the points inside the equation.

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

Simplify by order of operations.

$d= \sqrt{(3)^2+(-1)^2} = \sqrt{9+1} = \sqrt{10}$

The length of the line is $\sqrt{10}$ .

Report an Error

Example Question #40 : Points And Distance Formula

Find the distance between these two points using the distance formula:

(2, 6) and (-4, 8)

Possible Answers:

$\sqrt{40}$

$\sqrt{6}$

$\sqrt{10}$

Correct answer:

$\sqrt{40}$

Explanation:

To find the distance between two points using the distance formula, we use the following formula:

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

where (x_1, y_1) and (x_2, y_2) are the given points. So, we can substitute the points (2, 6) and (-4, 8) .

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

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

$d = \sqrt{36 + 4}$

$d = \sqrt{40}$

Therefore, the distance is $\sqrt{40}$ .

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 Next →

View Algebra Tutors

Vince
Certified Tutor

Salt Lake Community College, Associate in Science, Mathematics.

View Algebra Tutors

Dossevi
Certified Tutor

cole Ste Genevive Versailles, Bachelor of Science, Mathematics. Institut National Polytechnique de Grenoble, Master of Scienc...

View Algebra Tutors

Zhi Xuan
Certified Tutor

Queen's University, Bachelor, Engineering .

All Algebra 1 Resources

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

Popular Subjects

SSAT Tutors in Philadelphia, Reading Tutors in San Francisco-Bay Area, Algebra Tutors in Denver, MCAT Tutors in San Francisco-Bay Area, MCAT Tutors in Chicago, GRE Tutors in Atlanta, Reading Tutors in Chicago, Computer Science Tutors in Atlanta, Computer Science Tutors in San Francisco-Bay Area, SSAT Tutors in Washington DC

Popular Courses & Classes

SSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Denver, SSAT Courses & Classes in San Diego, GRE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Washington DC, ACT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Phoenix, GRE Courses & Classes in Boston, Spanish Courses & Classes in Phoenix

Popular Test Prep

GRE Test Prep in Chicago, GMAT Test Prep in Chicago, SAT Test Prep in Seattle, ISEE Test Prep in Washington DC, ACT Test Prep in Dallas Fort Worth, GMAT Test Prep in Phoenix, LSAT Test Prep in Phoenix, LSAT Test Prep in Atlanta, SAT Test Prep in San Diego, ACT 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)

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 #31 : Points And Distance Formula

Example Question #32 : Points And Distance Formula

Example Question #371 : Equations Of Lines

Example Question #34 : Points And Distance Formula

Example Question #35 : Points And Distance Formula

Example Question #36 : Points And Distance Formula

Example Question #37 : Points And Distance Formula

Example Question #38 : Points And Distance Formula

Example Question #39 : Points And Distance Formula

Example Question #40 : 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: