We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Coordinate Geometry

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : How To Find The Length Of A Line With Distance Formula

What is the length of a line with endpoints at (6,13) and (9,17) ?

Possible Answers:

$\frac{3}{4}$

$\frac{4}{3}$

625

Correct answer:

Explanation:

The formula for the length of a line is very similiar to the pythagorean theorem:

(x_2-x_1)^2+(y_2-y_1)^2=l^2

Plug in our given numbers to solve:

(x_2-x_1)^2+(y_2-y_1)^2=l^2

(17-13)^2+(9-6)^2=l^2

4^2+3^2=l^2

16+9=l^2

25=l^2

$\sqrt{25}=\sqrt{l^2}$

5=l

Report an Error

Example Question #21 : Coordinate Geometry

Find the distance between points (2,-4) and (14,-2) .

Possible Answers:

$\sqrt{148}$

$\sqrt{144}$

148

144

Correct answer:

$\sqrt{148}$

Explanation:

Use the distance formula:

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

Substitute the given points into the formula:

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

$d=\sqrt{148}$

Report an Error

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

What is the length of a line with endpoints of (2,-4) and (7,9) ?

Possible Answers:

3.7

13.9

17.1

14 7

Correct answer:

13.9

Explanation:

The distance formula is just a reworking of the Pythagorean theorem: $l=\sqrt{\Delta x^2+\Delta y^2}$

Expand that.

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

Plug in our given values.

$l=\sqrt{(7-2)^2+(9--4)^2}$

$l=\sqrt{(5)^2+(13)^2}$

$l=\sqrt{25+169}$

$l=\sqrt{194}$

l=13.9

Report an Error

Example Question #1366 : High School Math

What is the distance between (1,5) and (6,17) ?

Possible Answers:

Correct answer:

Explanation:

Let $P_{1}=(1,5)$ and $P_{2} = (6,17)$ .

The distance formula is given by $d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$ .

Substitute in the given points:

$d = \sqrt{(6-1)^{2}+(17-5)^{2}}=\sqrt{(5)^{2}+(12)^{2}}=\sqrt{25+144}=\sqrt{169}=13$

Report an Error

Example Question #23 : Algebra I

A line segment has endpoints at (2,3) and (-7,3) . What is the distance of this segment?

Possible Answers:

6.36

4.5

Correct answer:

Explanation:

To find the distance, we use the distance formula: $d^2=\Delta x^2+\Delta y^2$ .

Expand that:

d^2=(x_2-x_1)^2+(y_2-y_1)^2

Plug in our given values.

d^2=(-7-2)^2+(3-3)^2

d^2=(-9)^2+(0)^2

d^2=81+0

$\sqrt{d^2}=\sqrt{81}$

d=9

Report an Error

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

If a line has a length of , and the endpoints are (0,0) and (4,y) , what is the value of ?

Possible Answers:

1.5

Correct answer:

Explanation:

The formula for the length of a line, l, is the distance formula, which is very similar to the Pythagorean Theorem.

(x_2-x_1)^2+(y_2-y_1)^2=l^2

Note that the problem has already given us a value for the length of the line. That means l=5 . Plug in all of the given values and solve for the missing term.

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

4^2+y^2=5^2

16+y^2=25

Subtract $\small 16$ from both sides.

16+y^2-16=25-16

y^2=9

$\sqrt{y^2}=\sqrt{9}$

y=3

Report an Error

Example Question #22 : Coordinate Geometry

What is the distance between points (-2,4) and (12,3) ?

Possible Answers:

144

$\sqrt{197}$

$\sqrt{196}$

197

Correct answer:

$\sqrt{197}$

Explanation:

Use the distance formula:

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

Plug in the given points:

$d=\sqrt{(12-(-2)))^2+(3-4)^2}$

$d=\sqrt{197}$

Report an Error

Example Question #1 : Perpendicular Lines

Write an equation in slope-intercept form for the line that passes through $\left ( 3,1 \right )$ and that is perpendicular to a line which passes through the two points $\left ( 3,1 \right )$ and $\left ( -2,5 \right )$ .

Possible Answers:

$y=-\frac{4}{5}X+11$

$y=\frac{5}{4}X-\frac{11}{4}$

$y=\frac{5}{4}X+\frac{11}{4}$

y=5X-4

Correct answer:

$y=\frac{5}{4}X-\frac{11}{4}$

Explanation:

Find the slope of the line through the two points. It is $-\frac{4}{5}$ .

Since the slope of a perpendicular line is the negative reciprocal of the original line, the new line's slope is $\frac{5}{4}$ . Plug the slope and one of the points into the point-slope formula $y-y_{1}=m(x-x_{1})$ . Isolate for .

Report an Error

Example Question #2 : Perpendicular Lines

Find the equation of a line perpendicular to y=-3x+10

Possible Answers:

y=-3X+10

y=-3X-5

y=3X+2

$y=\frac{1}{3}X+8$

Correct answer:

$y=\frac{1}{3}X+8$

Explanation:

Since a perpendicular line has a slope that is the negative reciprocal of the original line, the new slope is $\frac{1}{3}$ . There is only one answer with the correct slope.

Report an Error

Example Question #3 : Perpendicular Lines

Find the equation (in slope-intercept form) of a line perpendicular to 3X+2Y=11 .

Possible Answers:

$y=3X+\frac{11}{2}$

$y=\frac{2}{3}X+\frac{11}{2}$

$y=2X+\frac{11}{2}$

$y=-\frac{3}{2}X+11$

Correct answer:

$y=\frac{2}{3}X+\frac{11}{2}$

Explanation:

First, find the slope of the original line, which is $-\frac{3}{2}$ . You can do this by isolating for so that the equation is in slope-intercept form. Once you find the slope, just replace the in the original equation withe the negative reciprocal (perpendicular lines have a negative reciprocal slope for each other). Thus, your answer is

$y=\frac{2}{3}X+\frac{11}{2}$

Report an Error

View Tutors

Angela
Certified Tutor

North Georgia College State University, Bachelor of Science, Special Education. North Georgia College State University, Mas...

View Tutors

Dereika
Certified Tutor

Southern University and A & M College, Bachelor of Science, Accounting. Grand Canyon University, Master of Science, Accounting.

View Tutors

Alexis
Certified Tutor

CUNY Lehman College, Bachelor in Arts, Linguistics.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Dallas Fort Worth, Statistics Tutors in Chicago, Biology Tutors in Houston, GRE Tutors in Miami, Physics Tutors in Boston, SAT Tutors in Miami, SAT Tutors in New York City, MCAT Tutors in Houston, Calculus Tutors in Philadelphia, Spanish Tutors in Boston

Popular Courses & Classes

SAT Courses & Classes in Phoenix, LSAT Courses & Classes in Boston, Spanish Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Chicago, Spanish Courses & Classes in Miami, SSAT Courses & Classes in Atlanta, SSAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Chicago, GRE Courses & Classes in Houston

Popular Test Prep

GRE Test Prep in Boston, SSAT Test Prep in Houston, MCAT Test Prep in Chicago, SSAT Test Prep in Los Angeles, LSAT Test Prep in Denver, ISEE Test Prep in Philadelphia, SAT Test Prep in Houston, MCAT Test Prep in Philadelphia, SSAT Test Prep in Seattle, ACT Test Prep in New York City

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

High School Math : Coordinate Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #4 : How To Find The Length Of A Line With Distance Formula

Example Question #21 : Coordinate Geometry

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

Example Question #1366 : High School Math

Example Question #23 : Algebra I

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

Example Question #22 : Coordinate Geometry

Example Question #1 : Perpendicular Lines

Example Question #2 : Perpendicular Lines

Example Question #3 : Perpendicular Lines

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: