Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Quantitative : Lines

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

Create An Account

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #81 : Plane Geometry

What is the slope of a line that passes through points (4.5,2.5) and (3.5, 6.5) ?

Possible Answers:

$\frac{1}{4}$

$-\frac{1}{4}$

Correct answer:

Explanation:

The equation for solving for the slope of a line is $m=\frac{y2-y1}{x2-x1}$ .

Thus, if (x1,y1)=(4.5, 2.5) and (x2,y2)=(3.5,6.5) , then:

$m=\frac{6.5-2.5}{3.5-4.5}=\frac{4}{-1}=-4$

Report an Error

Example Question #91 : Geometry

What is the slope of a line that passes through points (4,12) and (8, 20) ?

Possible Answers:

0.5

2.5

Correct answer:

Explanation:

The equation for solving for the slope of a line is $m=\frac{y2-y1}{x2-x1}$ .

Thus, if (x1,y1)=(4,12) and (x2,y2)=(8,20) , then:

$m=\frac{20-12}{8-4}=\frac{8}{4}=2$

Report an Error

Example Question #92 : Plane Geometry

Tangents 1

Figure NOT drawn to scale

In the above figure, $\overline{TN}$ and $\overline{TO}$ are tangent segments. The ratio of the length of $\overarc{NPO}$ to that of $\overarc{N O}$ is 5 to 3. Which is the greater quantity?

(a) $m \angle NTO$

(b) $30 ^{\circ }$

Possible Answers:

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

(a) and (b) are equal

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(a) is the greater quantity

Explanation:

For the sake of simplicity, let us assume that the lengths of $\overarc{NPO}$ and $\overarc{N O}$ are 5 and 3; this reasoning depends only on their ratio and not their actual length. The circumference of the circle is the sum of the lengths, which is 8, so $\overarc{NPO}$ and $\overarc{N O}$ comprise $\frac{5}{8}$ and $\frac{3}{8}$ of the circle, respectively. Therefore,

$m \overarc{NPO} = \frac{5}{8} \cdot 360 ^{\circ } = 225 ^{\circ }$ ; and

$m \overarc{N O} = \frac{3}{8} \cdot 360 ^{\circ } = 135 ^{\circ }$ .

If two tangents are drawn to a circle, the measure of the angle they form is half the difference of the measures of the arcs they intercept, so

$m \angle NTO = \frac{1}{2}(m \overarc{NPO} - m \overarc{N O} ) = \frac{1}{2}(225 ^{\circ }- 135^{\circ } ) = \frac{1}{2}(90^{\circ } ) = 45^{\circ }$

This is greater than $30 ^{\circ }$ .

Report an Error

Example Question #1 : How To Find A Ray

Which is the greater quantity?

(a) The length of the line segment connecting (0,0) and (a,b)

(b) The length of the line segment connecting (a,0) and (0,b)

Possible Answers:

(a) is greater.

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Correct answer:

(a) and (b) are equal.

Explanation:

(a) The length of the line segment connecting (0,0) and (a,b) is

$\sqrt{(a -0)^{2}+(b -0)^{2} } = \sqrt{a^{2}+b^{2} }$ .

(b) The length of the line segment connecting (a,0) and (0,b) is

$\sqrt{(a -0)^{2}+(0-b)^{2} } = \sqrt{a^{2}+\left ( - b \right ) ^{2} }= \sqrt{a^{2}+b^{2} }$ .

The segments have equal length.

Report an Error

View Tutors

Danielle
Certified Tutor

Northwestern University, Bachelors, Journalism. Tulane University of Louisiana, Master of Science, Finance.

View Tutors

Cheryl
Certified Tutor

Palm Beach Atlantic University-West Palm Beach, Bachelor of Science, Business Administration and Management. Southern New Ham...

View Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Los Angeles, ISEE Tutors in New York City, Chemistry Tutors in San Francisco-Bay Area, GMAT Tutors in Washington DC, Calculus Tutors in San Diego, Statistics Tutors in Phoenix, GRE Tutors in San Francisco-Bay Area, English Tutors in New York City, ISEE Tutors in Denver, Computer Science Tutors in Houston

Popular Courses & Classes

GMAT Courses & Classes in Boston, ACT Courses & Classes in Phoenix, GRE Courses & Classes in Boston, ISEE Courses & Classes in Miami, LSAT Courses & Classes in Houston, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in Miami, GRE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Denver, SAT Courses & Classes in Miami

Popular Test Prep

SSAT Test Prep in Philadelphia, LSAT Test Prep in Washington DC, LSAT Test Prep in Phoenix, SSAT Test Prep in Seattle, GRE Test Prep in Boston, SAT Test Prep in New York City, MCAT Test Prep in Denver, LSAT Test Prep in Philadelphia, LSAT Test Prep in Los Angeles, SAT Test Prep in Boston

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 Upper Level Quantitative : Lines

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #81 : Plane Geometry

Example Question #91 : Geometry

Example Question #92 : Plane Geometry

Example Question #1 : How To Find A Ray

All ISEE Upper Level Quantitative Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: