Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Geometry : Expressing Geometric Properties with Equations

Study concepts, example questions & explanations for Common Core: High School - Geometry

Create An Account

All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?
Plot1

Possible Answers:

$\left(x + 7\right)^{2} + \left(y - 2\right)^{2} = 4$

$\left(x - 7\right)^{2} + \left(y - 2\right)^{2} = 16$

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$

$\left(x - 7\right)^{2} + \left(y + 2\right)^{2} = 16$

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 4$

Correct answer:

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot1

we can see that the center is at

$\left ( -7, -2\right )$

The next step it to find the radius. Recall the radius is the distance from the center of the circle to any point on the edge of the circle.

From looking at the picture, we can see that the radius is 4. With this information, we can plug it into the general circle equation

The general circle equation is,

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ . When we plug in the values, we get

$\left(x + 7\right)^{2} + \left(y + 2\right)^{2} = 16$

Report an Error

Example Question #2 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?
Plot2

Possible Answers:

$\left(x + 9\right)^{2} + \left(y - 5\right)^{2} = 6$

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 6$

$\left(x - 9\right)^{2} + \left(y + 5\right)^{2} = 36$

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$

$\left(x - 9\right)^{2} + \left(y - 5\right)^{2} = 36$

Correct answer:

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot2

we can see that the center is at $\left ( -9, -5\right )$ .

The next step it to find the radius. Recall the radius is the distance from the center of the circle to any point of the circle's edge.

From looking at the picture, we can see that the radius is 6.

With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ .

When we plug in the values, we get

$\left(x + 9\right)^{2} + \left(y + 5\right)^{2} = 36$

Report an Error

Example Question #3 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?

Plot3

Possible Answers:

$\left(x + 9\right)^{2} + \left(y - 2\right)^{2} = 6$

$\left(x - 9\right)^{2} + \left(y - 2\right)^{2} = 36$

Correct answer:

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot3

we can see that the center is at $\left ( -9, -2\right )$ .

The next step it to find the radius From looking at the picture, we can see that the radius is 6.

With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ .

We plug in the values, we get

$\left(x + 9\right)^{2} + \left(y + 2\right)^{2} = 36$

Report an Error

Example Question #4 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?

Plot4

Possible Answers:

$\left(x - 10\right)^{2} + \left(y + 4\right)^{2} = 16$

$\left(x + 10\right)^{2} + \left(y + 4\right)^{2} = 4$

$\left(x + 10\right)^{2} + \left(y - 4\right)^{2} = 16$

$\left(x + 10\right)^{2} + \left(y - 4\right)^{2} = 4$

$\left(x - 10\right)^{2} + \left(y - 4\right)^{2} = 16$

Correct answer:

$\left(x + 10\right)^{2} + \left(y - 4\right)^{2} = 16$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot4

we can see that the center is at $\left ( -10, 4\right )$

The next step it to find the radius From looking at the picture, we can see that the radius is 4.

With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$

We plug in the values, we get

$\left(x + 10\right)^{2} + \left(y - 4\right)^{2} = 16$

Report an Error

Example Question #5 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?
Plot5

Possible Answers:

$\left(x - 4\right)^{2} + \left(y - 2\right)^{2} = 81$

$\left(x + 4\right)^{2} + \left(y + 2\right)^{2} = 81$

$\left(x + 4\right)^{2} + \left(y - 2\right)^{2} = 9$

$\left(x + 4\right)^{2} + \left(y + 2\right)^{2} = 9$

$\left(x - 4\right)^{2} + \left(y + 2\right)^{2} = 81$

Correct answer:

$\left(x + 4\right)^{2} + \left(y + 2\right)^{2} = 81$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture, we can see that the center is at $\left ( -4, -2\right )$

The next step it to find the radius. From looking at the picture,

Plot5

we can see that the radius is 9.

With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ .

We plug in the values, we get

$\left(x + 4\right)^{2} + \left(y + 2\right)^{2} = 81$

Report an Error

Example Question #6 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?
Plot6

Possible Answers:

$\left(x + 3\right)^{2} + \left(y - 3\right)^{2} = 1$

$\left(x - 3\right)^{2} + \left(y + 3\right)^{2} = 1$

$\left(x + 3\right)^{2} + \left(y + 3\right)^{2} = 1$

$\left(x - 3\right)^{2} + \left(y - 3\right)^{2} = 1$

Correct answer:

$\left(x + 3\right)^{2} + \left(y - 3\right)^{2} = 1$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot6

we can see that the center is at $\left ( -3, 3\right )$

The next step it to find the radius From looking at the picture, we can see that the radius is 1.

With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$

We plug in the values, we get

$\left(x + 3\right)^{2} + \left(y - 3\right)^{2} = 1$

Report an Error

Example Question #7 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?
Plot7

Possible Answers:

Correct answer:

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot7

we can see that the center is at $\left ( 2, 2\right )$

The next step it to find the radius From looking at the picture, we can see that the radius is 4.

With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$

We plug in the values, we get

$\left(x - 2\right)^{2} + \left(y - 2\right)^{2} = 16$

Report an Error

Example Question #8 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?

Plot8

Possible Answers:

$\left(x + 10\right)^{2} + \left(y + 3\right)^{2} = 6$

$\left(x + 10\right)^{2} + \left(y - 3\right)^{2} = 6$

$\left(x - 10\right)^{2} + \left(y - 3\right)^{2} = 36$

$\left(x - 10\right)^{2} + \left(y + 3\right)^{2} = 36$

$\left(x + 10\right)^{2} + \left(y + 3\right)^{2} = 36$

Correct answer:

$\left(x + 10\right)^{2} + \left(y + 3\right)^{2} = 36$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle If we look at the picture,

Plot8

we can see that the center is at $\left ( -10, -3\right )$

The next step it to find the radius. From looking at the picture, we can see that the radius is 6. With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$ .

We plug in the values, we get

$\left(x + 10\right)^{2} + \left(y + 3\right)^{2} = 36$

Report an Error

Example Question #9 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?

Plot9

Possible Answers:

$\left(x - 1\right)^{2} + \left(y - 7\right)^{2} = 2$

$\left(x + 1\right)^{2} + \left(y + 7\right)^{2} = 4$

$\left(x + 1\right)^{2} + \left(y - 7\right)^{2} = 4$

$\left(x - 1\right)^{2} + \left(y + 7\right)^{2} = 2$

$\left(x - 1\right)^{2} + \left(y - 7\right)^{2} = 4$

Correct answer:

$\left(x - 1\right)^{2} + \left(y - 7\right)^{2} = 4$

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,

Plot9

we can see that the center is at $\left ( 1, 7\right )$

The next step it to find the radius. From looking at the picture, we can see that the radius is 2. With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$

We plug in the values, we get

$\left(x - 1\right)^{2} + \left(y - 7\right)^{2} = 4$

Report an Error

Example Question #10 : Expressing Geometric Properties With Equations

What is the equation of the circle shown below?

Plot10

Possible Answers:

$\left(x + 5\right)^{2} + \left(y + 6\right)^{2} = 2$

$\left(x - 5\right)^{2} + \left(y - 6\right)^{2} = 4$

$\left(x - 5\right)^{2} + \left(y + 6\right)^{2} = 4$

Correct answer:

Explanation:

In order to find the equation, we must find the coordinates of the center of the circle.

If we look at the picture,
Plot10
we can see that the center is at $\left ( -5, 6\right )$

The next step it to find the radius. From looking at the picture, we can see that the radius is 2. With this information, we can plug it into the general circle equation.

The general circle equation is

$\left(- a + x\right)^{2} + \left(- b + y\right)^{2} = c^{2}$

Now we substitute for $\uptext{a}$ , $\uptext{b}$ , and $\uptext{c}$

We plug in the values, we get

$\left(x + 5\right)^{2} + \left(y - 6\right)^{2} = 4$

Report an Error

View Tutors

Katherine
Certified Tutor

University of Wisconsin-Madison, Bachelors, Philosophy /Chemistry. University of Wisconsin-Madison, Masters, Curriculum and I...

View Tutors

Bhawna
Certified Tutor

Conestoga College, Master's/Graduate, Computer Science.

View Tutors

Kayla
Certified Tutor

Stephen F Austin State University, Bachelor in Arts, History.

All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Washington DC, Spanish Tutors in Atlanta, SSAT Tutors in Miami, Algebra Tutors in San Diego, Biology Tutors in Washington DC, English Tutors in San Francisco-Bay Area, Biology Tutors in Miami, Reading Tutors in Miami, Biology Tutors in Los Angeles, ACT Tutors in Atlanta

Popular Courses & Classes

LSAT Courses & Classes in Houston, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in Los Angeles, ACT Courses & Classes in Houston, Spanish Courses & Classes in New York City, ISEE Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Los Angeles, GRE Courses & Classes in Boston, MCAT Courses & Classes in Washington DC, MCAT Courses & Classes in Miami

Popular Test Prep

ACT Test Prep in Houston, LSAT Test Prep in Atlanta, SSAT Test Prep in Phoenix, SAT Test Prep in Dallas Fort Worth, ISEE Test Prep in New York City, SAT Test Prep in New York City, ISEE Test Prep in Miami, SAT Test Prep in Boston, SSAT Test Prep in San Diego, GMAT 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

Common Core: High School - Geometry : Expressing Geometric Properties with Equations

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #1 : Expressing Geometric Properties With Equations

Example Question #2 : Expressing Geometric Properties With Equations

Example Question #3 : Expressing Geometric Properties With Equations

Example Question #4 : Expressing Geometric Properties With Equations

Example Question #5 : Expressing Geometric Properties With Equations

Example Question #6 : Expressing Geometric Properties With Equations

Example Question #7 : Expressing Geometric Properties With Equations

Example Question #8 : Expressing Geometric Properties With Equations

Example Question #9 : Expressing Geometric Properties With Equations

Example Question #10 : Expressing Geometric Properties With Equations

All Common Core: High School - Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: