We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Intermediate Geometry : Coordinate Geometry

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

Example Question #1 : Midpoint Formula

What is the midpoint between (-1,3) and (7,-5) ?

Possible Answers:

(3,-1)

(4,-4)

(3,0)

(4,-1)

(2,2)

Correct answer:

(3,-1)

Explanation:

The midpoint is given by taking the mean, or average, of the and coordinates separately.

Let $P_{1}=\left ( 7,5 \right )$ and $P_{2} = \left (-1,3 \right )$

So the midpoint formula becomes $\frac{x_{1}\ +\ x_{2}}{2}= \frac{7-1}{2}=3$ and $\frac{y_{1}+y_{2}}{2}= \frac{-5 +3}{2}=-1$

So the midpoint is (3,-1)

Report an Error

Example Question #1 : Coordinate Geometry

What is the midpoint of a line segment connecting the points $\left ( -5,6 \right )$ and $\left ( -3,2 \right )\ ?$

Possible Answers:

$\left ( -1,4 \right )$

$\left ( -4,4 \right )$

$\left ( -4,2 \right )$

$\left ( -1,2 \right )$

Correct answer:

$\left ( -4,4 \right )$

Explanation:

Use the midpoint formula:

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=midpoint$

$(\frac{-5+(-3)}{2}, \frac{6+2}{2})=(\frac{-8}{2}, \frac{8}{2})=(-4,4)$

Report an Error

Example Question #1 : Midpoint Formula

Given two points $\left ( -3,-3 \right )$ and $\left ( -1,1 \right )$ and a line segment that connects the two.

What is the midpoint of the line segment? Addtionally, what is the length of the line segment?

Possible Answers:

Midpoint: $\left ( -1,-1 \right )$

Length: $4\sqrt3$

Midpoint: $\left ( -2,-1 \right )$

Length: $\sqrt5$

Midpoint: $\left ( -2,-1 \right )$

Length: $2\sqrt{5}$

Midpoint: $\left ( -1,-2 \right )$

Length:

Midpoint: $\left ( -1,-2 \right )$

Length: $2\sqrt5$

Correct answer:

Midpoint: $\left ( -2,-1 \right )$

Length: $2\sqrt{5}$

Explanation:

The midpoint formula is as follows:

$midpoint = (\frac{x_1 +x_2}{2},\frac{y_1+y_2}{2})$

This makes sense; it is as simple as the average of the and components of each point.

For this problem, $x_1=-3,x_2=-1,y_1=-3,and\: y_2=1$ .

So the midpoint is $\left ( -2,-1 \right )$

The distance formula is as follows:

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

The order you put the first and second components of each point does NOT matter, when a positive or negative number is squared, it will always come out positive.

$(2)^2=4\; and\; (-4)^2=16$

So the distance is $\sqrt{(-3+1)^2+(-3-1)^2} =\sqrt{4+16}=\sqrt{20}=2\sqrt{5}$

Report an Error

Example Question #2 : Midpoint Formula

Find the midpoint of a line segment going from (-2,-9) to (-6,-1) .

Possible Answers:

(-4,-5)

(3,5)

(-1,3)

(2,4)

(-4,4)

Correct answer:

(-4,-5)

Explanation:

To find the midpoint of a line segment, you must find the mean of the x values and the mean of the y values.

Our x values are and to find their mean, we do (-2+-6)/2=-4 .

Our y values are and , so our mean is (-9+-1)/2=-5 . Therefore, our midpoint must be (-4,-5) .

Report an Error

Example Question #3 : Midpoint Formula

Find the coordinate of the midpoint of the line segment connecting the pair of points

(2, 2) and (4, 12) .

Possible Answers:

(1, 5)

(3, 7)

(2, 7)

Cannot be determined

Correct answer:

(3, 7)

Explanation:

The coordinate of the midpoint of the line segment connecting a pair of points is

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

So for the pair of points (x_1,y_1)=(2,2) and (x_2,y_2)=(4,12) ,

we get:

$\left(\frac{2+4}{2}, \frac{2+12}{2}\right)=(3, 7)$

Report an Error

Example Question #1 : Midpoint Formula

Find the coordinate of the midpoint of the line segment connecting the pair of points

(0, 0) and (8, 0) .

Possible Answers:

Cannot be determined

(0, 4))

(-4, 0)

(4, 0)

Correct answer:

(4, 0)

Explanation:

The coordinate of the midpoint of the line segment connecting a pair of points is

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ .

So for the pair of points (x_1,y_1)=(0, 0) and (x_2,y_2)=(8, 0)

we get,

$\left(\frac{0+8}{2}, \frac{0+0}{2}\right)=(4, 0)$

Report an Error

Example Question #2 : Midpoint Formula

A line extends from the origin to $\small (14, -2)$ . What is its midpoint?

Possible Answers:

$\small (7,-1)$

$\small (28, -4)$

$\small (1,-7)$

$\small (7, 1 )$

$\small (-7, -1)$

Correct answer:

$\small (7,-1)$

Explanation:

The origin is the point $\small (0,0)$ . We can use the regular midpoint formula with $\small (0,0)$ as $\small (x_{1}, y_{1})$ and the given point $\small (14, -2)$ as $\small (x_{2}, y_{2})$ :

$\small (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

$\small (\frac{0+14}{2} , \frac{0+-2}{2})$

$\small (\frac{14}{2}, \frac{-2}{2}) = (7, -1)$

Note that since the first point is the origin, we're averaging these points with 0, or in other words just dividing by 2.

Report an Error

Example Question #8 : Midpoint Formula

There is a line segment between the two points (5, 10) and (3, 6). What formula will give you the correct mid-point of the line segment?

Possible Answers:

$\Big( {5-2} \; ,{10-2} \Big )$

$\Big( \frac{5+10}{2} \; , \frac{3+6}{2} \Big )$

$\Big( \frac{5-3}{2} \; , \frac{10-6}{2} \Big )$

$\Big( \frac{5-10}{2} \; , \frac{3-6}{2} \Big )$

$\Big( \frac{5+3}{2} \; , \frac{10+6}{2} \Big )$

Correct answer:

$\Big( \frac{5+3}{2} \; , \frac{10+6}{2} \Big )$

Explanation:

To find the mid-point given two points on the coordinate plane you are basically finding the average of the x-values and the average of the y-values. To do this follow the formula below:

$\Big( \frac{x_{1}+ x_{2}}{2} \; , \frac{y_{1}+y_{2}}{2} \Big )$

With our points this gives:

$\Big( \frac{5+3}{2} \; , \frac{10+6}{2} \Big )$

Report an Error

Example Question #7 : Midpoint Formula

A line has endpoints at (4,5) and (-6,8). Where is its midpoint?

Possible Answers:

$\left(\frac{13}{2},-1\right)$

$\left(1,\frac{13}{2}\right)$

$\left(\frac{-13}{2},-1\right)$

$\left(\frac{-13}{2},1\right)$

$\left(-1,\frac{13}{2}\right)$

Correct answer:

$\left(-1,\frac{13}{2}\right)$

Explanation:

The midpoint is the point that is equidistant from each endpoint point.

We find it using a formula that computes the average of the x and y coordinates.

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$\left(\frac{4+(-6)}{2},\frac{5+8}{2}\right)$

$\left(\frac{-2}{2},\frac{13}{2}\right)$

$\mathbf{\left(-1,\frac{13}{2}\right)}$

Report an Error

Example Question #3 : Midpoint Formula

A line segment has the endpoints (2, 4) and (1, 8) . What is the midpoint of this line segment?

Possible Answers:

$(\frac{3}{2},6)$

$(\frac{1}{2},12)$

$(\frac{5}{2},2)$

(6, 3)

Correct answer:

$(\frac{3}{2},6)$

Explanation:

Recall the formula for finding a midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{2+1}{2}, \frac{4+8}{2})=(\frac{3}{2}, 6)$

Report an Error

View Tutors

George
Certified Tutor

Pensacola State College, Bachelor in Arts, Mathematics.

View Tutors

Krittika
Certified Tutor

University of Dhaka, Master's/Graduate, Statistics. University of Waterloo, Master's/Graduate, Biostatistics.

View Tutors

Jordan
Certified Tutor

University of Maryland-College Park, Bachelor of Science, Physics. University of Maryland-College Park, Bachelor in Arts, Ger...

All Intermediate Geometry Resources

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

Popular Subjects

Algebra Tutors in Houston, MCAT Tutors in Los Angeles, Physics Tutors in Miami, MCAT Tutors in Philadelphia, GMAT Tutors in Atlanta, English Tutors in Houston, LSAT Tutors in Philadelphia, English Tutors in Philadelphia, Calculus Tutors in Chicago, French Tutors in Seattle

Popular Courses & Classes

SAT Courses & Classes in Atlanta, Spanish Courses & Classes in Seattle, LSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Miami, GMAT Courses & Classes in Phoenix, SSAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Los Angeles, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Denver

Popular Test Prep

GRE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Phoenix, GRE Test Prep in Phoenix, GMAT Test Prep in Phoenix, SAT Test Prep in New York City, ACT Test Prep in Miami, MCAT Test Prep in Phoenix, MCAT Test Prep in Chicago, MCAT Test Prep in Seattle, GRE 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

Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : Midpoint Formula

Example Question #1 : Coordinate Geometry

Example Question #1 : Midpoint Formula

Example Question #2 : Midpoint Formula

Example Question #3 : Midpoint Formula

Example Question #1 : Midpoint Formula

Example Question #2 : Midpoint Formula

Example Question #8 : Midpoint Formula

Example Question #7 : Midpoint Formula

Example Question #3 : Midpoint Formula

All Intermediate Geometry Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: