Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Middle Level Quantitative : Geometry

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

Create An Account

All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 … 26 27 Next →

Example Question #1 : Geometry

Give the equation of the line through point (1,4) that has slope $-\frac{1}{5}$ .

Possible Answers:

$y = -\frac{1}{5}x + 4$

y = -5x + 4

$y = -\frac{1}{5}x + \frac{21}{5}$

$y = \frac{1}{5}x - \frac{19}{5}$

y = -5x + 9

Correct answer:

$y = -\frac{1}{5}x + \frac{21}{5}$

Explanation:

Use the point-slope formula with $m = -\frac{1}{5}, x_{1}= 1, y_{1} = 4$

$y -y _{1} = m (x -x _{1} )$

$y -4 = -\frac{1}{5} (x -1 )$

$y -\frac{20}{5} = -\frac{1}{5} x + \frac{1}{5}$

$y = -\frac{1}{5} x + \frac{21}{5}$

Report an Error

Example Question #1 : Coordinate Geometry

Which is the greater quantity?

(A) The slope of the line 2x+y = 15

(B) The slope of the line 3x+y = 15

Possible Answers:

(A) and (B) are equal

(B) is greater

It is impossible to determine which is greater from the information given

(A) is greater

Correct answer:

(A) is greater

Explanation:

Rewrite each in the slope-intercept form, y = mx + b ; will be the slope.

2x+y = 15

2x+y -2x = 15-2x

y=15-2x

y = -2x+ 15

The slope of this line is m = -2 .

3x+y = 15

3x+y -3x = 15-3x

y=15-3x

y = -3x+ 15

The slope of this line is m = -3 .

Since -2 > -3 , (A) is greater.

Report an Error

Example Question #1 : Coordinate Geometry

Which is the greater quantity?

(A) The slope of the line 4x - 2y = 10

(B) The slope of the line y - 2x = 7

Possible Answers:

(B) is greater

(A) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

Correct answer:

(A) and (B) are equal

Explanation:

Rewrite each in the slope-intercept form, y = mx + b ; will be the slope.

4x - 2y = 10

4x - 2y -4x = 10-4x

- 2y = -4x+ 10

$- 2y \div (-2) =\left ( -4x+ 10 \right )\div (-2)$

y = 2x -5

The slope of the line of 4x - 2y = 10 is m = 2

y - 2x = 7

y - 2x + 2x = 7+ 2x

y = 2x + 7

The slope of the line of y - 2x = 7 is also m = 2

The slopes are equal.

Report an Error

Example Question #4 : How To Find A Line On A Coordinate Plane

and are positive integers, and A > B . Which is the greater quantity?

(a) The slope of the line on the coordinate plane through the points (A+ 1, B+ 1 ) and (A-1, B- 1 ) .

(b) The slope of the line on the coordinate plane through the points (B- 1, A- 1 ) and (B+1, A+ 1 ) .

Possible Answers:

It is impossible to determine which is greater from the information given

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(a) and (b) are equal

Explanation:

The slope of a line through the points (A+ 1, B+ 1 ) and (A-1, B- 1 ) can be found by setting

$x_{1} = A-1,y_{1} = B - 1, x_{2} = A+1, y_{2} = B+ 1$

in the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$= \frac{ (B+ 1)- (B- 1)}{ (A+ 1)- (A- 1)}$

$= \frac{ B-B+ 1+1}{ A-A + 1 + 1}$

$= \frac{ 2}{ 2}$

The slope of a line through the points (B- 1, A- 1 ) and (B+1, A+ 1 ) can be found similarly:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$= \frac{(A+ 1)- (A- 1) }{ (B+ 1)- (B- 1) }$

$= \frac{A-A + 1+1}{B-B + 1 + 1}$

$= \frac{ 2}{ 2}$

The lines have the same slope.

Report an Error

Example Question #5 : How To Find A Line On A Coordinate Plane

A line passes through the points with coordinates (A, B) and (-A, B ) , where A > B >0 . Which expression is equal to the slope of the line?

Possible Answers:

Undefined

$\frac{A}{B}$

$\frac{B}{A}$

Correct answer:

Explanation:

The slope of a line through the points (A, B) and (-A, B ) , can be found by setting

$x_{1} = -A,y_{1} =B, x_{2} = A, y_{2} = B$ :

in the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m = \frac{B-B}{A - (-A)} = \frac{0}{A+A} = \frac{0}{2A} = 0$

Report an Error

Example Question #1 : Geometry

Choose the best answer from the four choices given.

The point (15, 6) is on which of the following lines?

Possible Answers:

$y=\frac{-1}{2}x+7$

$y=\frac{1}{2}x-7$

$y=-\frac{2}{3}x+4$

$y=\frac{2}{3}x-4$

Correct answer:

$y=\frac{2}{3}x-4$

Explanation:

For this problem, simply plug in the values for the point (15,6) into the different equations (15 for the -value and 6 for the -value) to see which one fits.

$(6)=\frac{1}{2}(15)-7$ (NO)

$(6)=\frac{2}{3}(15)-4$ (YES!)

$(6)=\frac{-1}{2}(15)+7$ (NO)

$(6)=\frac{-2}{3}(15)+4$ (NO)

Report an Error

Example Question #1 : How To Find The Points On A Coordinate Plane

Choose the best answer from the four choices given.

What is the point of intersection for the following two lines?

$y=\frac{3}{4}x-11$

$y=\frac{-5}{6}x+8$

Possible Answers:

$\left ( 12,-2 \right )$

$\left ( 8,-5 \right )$

$\left ( 6,3 \right )$

$\left ( 0,-11 \right )$

Correct answer:

$\left ( 12,-2 \right )$

Explanation:

At the intersection point of the two lines the - and - values for each equation will be the same. Thus, we can set the two equations as equal to each other:

$\frac{3}{4}x-11=\frac{-5}{6}x+8$

$\frac{3}{4}x=\frac{-5}{6}x+19$

$\frac{9}{12}x=\frac{-10}{12}x+19$

$\frac{19}{12}x=19$

$(\frac{12}{19})(\frac{19}{12}x)=19 (\frac{12}{19})$

$\large x=12$

$y=\frac{3}{4}(12)-11= -2$

point of intersection $=\left ( 12,-2 \right )$

Report an Error

Example Question #3 : How To Find The Points On A Coordinate Plane

Choose the best answer from the four choices given.

What is the -intercept of the line represented by the equation

$y=\frac{7}{9}x-3\ ?$

Possible Answers:

$3\frac{6}{7}$

$-3\frac{6}{7}$

Correct answer:

$3\frac{6}{7}$

Explanation:

In the formula y=mx+b , the y-intercept is represented by (because if you set to zero, you are left with y=b ).

Thus, to find the -intercept, set the value to zero and solve for .

$0=\frac{7}{9}x-3$

$\frac{-7}{9}x=-3$

$(\frac{-9}{7})\frac{-7}{9}x=-3 (\frac{-9}{7})$

$x=\frac{27}{7}=3\frac{6}{7}$

Report an Error

Example Question #1 : Coordinate Geometry

The ordered pair (-1,4) is in which quadrant?

Possible Answers:

Quadrant I

Quadrant V

Quadrant II

Quadrant III

Quadrant IV

Correct answer:

Quadrant II

Explanation:

There are four quadrants in the coordinate plane. Quadrant I is the top right, and they are numbered counter-clockwise. Since the x-coordinate is , you go to the left one unit (starting from the origin). Since the y-coordinate is , you go upwards four units. Therefore, you are in Quadrant II.

Report an Error

Example Question #1 : Coordinate Geometry

If angles s and r add up to 180 degrees, which of the following best describes them?

Possible Answers:

Complementary

Acute

Obtuse

Supplementary.

Correct answer:

Supplementary.

Explanation:

Two angles that are supplementary add up to 180 degrees. They cannot both be acute, nor can they both be obtuse. Therefore, "Supplementary" is the correct answer.

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 26 27 Next →

View Tutors

Aaron
Certified Tutor

Portland State University, Bachelors, Economics. Portland State University, Masters, Environmental and Resource Management.

View Tutors

Neil
Certified Tutor

Florida State University, Bachelor in Arts, Philosophy.

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Houston, SSAT Tutors in Houston, Statistics Tutors in Atlanta, GRE Tutors in New York City, GMAT Tutors in Chicago, GMAT Tutors in Houston, ACT Tutors in Atlanta, Math Tutors in Los Angeles, Computer Science Tutors in Dallas Fort Worth, Computer Science Tutors in Seattle

Popular Courses & Classes

MCAT Courses & Classes in Boston, SAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Boston, SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Atlanta, SAT Courses & Classes in Seattle, SSAT Courses & Classes in Houston, ACT Courses & Classes in Boston, ISEE Courses & Classes in Chicago, GMAT Courses & Classes in Atlanta

Popular Test Prep

ACT Test Prep in Boston, ISEE Test Prep in Houston, GMAT Test Prep in Philadelphia, GRE Test Prep in Seattle, SAT Test Prep in San Diego, SAT Test Prep in Miami, MCAT Test Prep in New York City, GMAT Test Prep in Atlanta, GRE Test Prep in Atlanta, MCAT Test Prep in Seattle

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

ISEE Middle Level Quantitative : Geometry

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #1 : Geometry

Example Question #1 : Coordinate Geometry

Example Question #1 : Coordinate Geometry

Example Question #4 : How To Find A Line On A Coordinate Plane

Example Question #5 : How To Find A Line On A Coordinate Plane

Example Question #1 : Geometry

Example Question #1 : How To Find The Points On A Coordinate Plane

Example Question #3 : How To Find The Points On A Coordinate Plane

Example Question #1 : Coordinate Geometry

Example Question #1 : Coordinate Geometry

All ISEE Middle Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: