Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Distance Formula

What is the distance of the line drawn between points (–1,–2) and (–9,4)?

Possible Answers:

√5

Correct answer:

Explanation:

The answer is 10. Use the distance formula between 2 points, or draw a right triangle with legs length 6 and 8 and use the Pythagorean Theorem.

Report an Error

Example Question #3 : Distance Formula

What is the distance between two points $\dpi{100} \small (6,14)$ and $\dpi{100} \small (-6,9)$ ?

Possible Answers:

$\dpi{100} \small -12$

$\dpi{100} \small 5$

$\dpi{100} \small 10\sqrt{3}$

$\dpi{100} \small 17$

$\dpi{100} \small 13$

Correct answer:

$\dpi{100} \small 13$

Explanation:

To find the distance between two points such as these, plot them on a graph.

Then, find the distance between the $\dpi{100} \small x$ units of the points, which is 12, and the distance between the $\dpi{100} \small y$ points, which is 5. The $\dpi{100} \small x$ represents the horizontal leg of a right triangle and the $\dpi{100} \small y$ represents the vertial leg of a right triangle. In this case, we have a 5,12,13 right triangle, but the Pythagorean Theorem can be used as well.

Report an Error

Example Question #4 : Distance Formula

What is the distance between $(1,3)\ and\ (5,6)$ ?

Possible Answers:

$5$

$7$

$4$

$6$

$8$

Correct answer:

$5$

Explanation:

Let $P_{1}(1,3)$ and $P_{2}(5,6)$ and use the distance formula:

$d = \sqrt{(x_{2} - x_{1})^2+(y_{2} - y_{1})^2}$

Report an Error

Example Question #5 : Distance Formula

What is the distance between the point (-12,35) and the origin?

Possible Answers:

Correct answer:

Explanation:

The distance between 2 points is found using the distance or Pythagorean Theorem. Because values are squared in the formula, distance can never be a negative value.

Report an Error

Example Question #6 : Distance Formula

Bill gets in his car and drives north for 30 miles at 40 mph. He then turns west and drives 40 mph for 40 minutes. Finally, he goes directly northeast 40 miles in 25 minutes.

Using the total distance traveled as a straight line ("as the crow flies") and the time spent traveling, which of the following is closest to Bill's average speed?

Possible Answers:

$27\ mph$

$32\ mph$

$30\ mph$

$40\ mph$

$35\ mph$

Correct answer:

$32\ mph$

Explanation:

Each part of the problem gives you 2 out of the 3 pieces of the rate/time/distance relationship, thus allowing you to find the third (if needed) by using the equation:

$Distance = rate\cdot time$

The problem is otherwise an application of geometry and the distance formula. We need to find the distance between 2 points, but we need to go step-by-step to find out where the final point is. The first two steps are relatively easy to follow. He travels 30 miles north. Now he turns west and travels for 40 minutes at 40 mph. This is $\frac{2}{3}$ of an hour, so we have $40\cdot \frac{2}{3}=\frac{80}{3}\ miles$ . Thus if we are looking at standard Cartesian coordinates (starting at the origin), we are now at the point $\left ( \frac{80}{3},30 \right )$ .

We are now on the last step: 40 miles northeast. We need to decipher this into - and - coordinate changes. To do this, we think of a triangle. Because we are moving directly northeast, this is a 45 degree angle to the horizontal. We can thus imagine a 45-45-90 triangle with a hypotenuse of 40. Now using the relationships on triangles we have:

$40^{2} = x^{2} + x^{2} = 2x^{2}\Rightarrow 40 = \sqrt{2x^{2}} = x\sqrt{2} \Rightarrow x = \frac{40}{\sqrt{2}} = 20\sqrt{2}$

So the final step moves us $20\sqrt{2}$ up and to the right. Moving this way from the point $\left ( \frac{80}{3},30 \right )$ leaves us at:

$\left ( \frac{80}{3}-20\sqrt{2}, 30+20\sqrt{2} \right ) \approx \left ( -1.6, 58.3\right )$

Using the distance formula for this point from the origin gives us a distance of ~58 miles.

Now for the time. We traveled 30 miles at 40 mph. This means we traveled for $\frac{30}{40}$ hours or 45 minutes.

We then traveled 40 mph for 40 minutes. Increasing our total time traveled to 85 minutes.

Finally, we traveled 40 miles in 25 minutes, leaving our total time traveled at 110 minutes. Returning to hours, we have $\frac{110}{60}$ hours or 1.83 hours.

Our final average speed traveled is then:

$\frac{58 miles}{1.83 hours} \approx 31.7 mph$

The closest answer to this value is 32 mph.

Report an Error

Example Question #7 : Distance Formula

Steven draws a line that is 13 units long. If $(-4,1)$ is one endpoint of the line, which of the following might be the other endpoint?

Possible Answers:

$(9,14)$

$(1,13)$

$(13,13)$

$(5,12)$

$(3,7)$

Correct answer:

$(1,13)$

Explanation:

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

Plug in $(-4,1)$ with each of the answer choices and solve.

Plug in $(1,13)$ :

$d=\sqrt{(1-(-4))^2+ (13-1)^2} = \sqrt{5^2+12^2}=\sqrt{25+144}=\sqrt{169}=13$

This is therefore the correct answer choice.

Report an Error

Example Question #8 : Distance Formula

What is the distance between the points (3,12) and (7,2) ?

Possible Answers:

$3\sqrt{5}$

$2\sqrt{29}$

$4\sqrt{2}$

Correct answer:

$2\sqrt{29}$

Explanation:

Plug the points into the distance formula and simplify:

distance² = (x₂ – x₁)² + (y₂ – y₁)² = (7 – 3)² + (2 – 12)² = 4² + 10² = 116

distance = √116 = √(4 * 29) = 2√29

Report an Error

Example Question #9 : Distance Formula

What is the distance between $(3,4)$ and $(8,16)$ ?

Possible Answers:

$12$

$23$

$20$

$13$

$17$

Correct answer:

$13$

Explanation:

The formula for the distance between two points is $d = \sqrt{(x_{2} - x_{1})^2+(y_{2} - y_{1})^2}$ .

Plug in the points:

$d=\sqrt{(8-3)^2+(16-4)^2}$

$d = \sqrt{5^2+12^2} = 13$

Report an Error

Example Question #9 : Distance Formula

Suppose a line is connected from two points. What is the distance of the line if the line is connected from (3,-9) to (-1,6) ?

Possible Answers:

$\sqrt{31}$

$\sqrt{241}$

$\sqrt{11}$

$\sqrt{19}$

$3\sqrt{17}$

Correct answer:

$\sqrt{241}$

Explanation:

Write the distance formula and substitute the values into the formula.

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

Let (x_1,y_1)=(3,-9) and (x_2,y_2)=(-1,6) .

Plugging in our coordinates into the distance formula we get the following.

$D=\sqrt{((-1)-3)^2+(6-(-9))^2}= \sqrt{(-4)^2+(15)^2}$

$D= \sqrt{16+225}=\sqrt{241}$

Report an Error

Example Question #11 : Distance Formula

Find the Distance of the line shown below:

Screen shot 2015 10 27 at 3.11.25 pm

Possible Answers:

$2\sqrt{5}$

$\sqrt{53}$

$\sqrt{13}$

Correct answer:

$\sqrt{53}$

Explanation:

The distance formula is $^{\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}}$ . In the graph shown above the coordinates are (-5,8) and (2,10) . When you plug the coordinates into the equation you get:

$\sqrt{(-5-2)^{2}+(8-10)^{2}}$ , which then simplifies to $\sqrt{(-7)^{2}+(2)^{2}}$

$\sqrt{49+4}=\sqrt{53}$ , because is a prime number there is no need to simplify.

Report an Error

View SAT Mathematics Tutors

Bill
Certified Tutor

SUNY Empire State College, Bachelors, General Sciences, Theater.

View SAT Mathematics Tutors

Chinedu
Certified Tutor

Federal University of Technology, Owerri, Bachelors, Chemical Engineering. University of Houston, Current Grad Student, Chemi...

View SAT Mathematics Tutors

Daniel
Certified Tutor

Stony Brook University, Bachelors, Biology, General. SUNY College of Optometry, PHD, Optometry.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

SSAT Courses & Classes in Houston, Spanish Courses & Classes in Houston, LSAT Courses & Classes in Seattle, SAT Courses & Classes in Houston, MCAT Courses & Classes in Seattle, MCAT Courses & Classes in Philadelphia, SAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Miami, ACT Courses & Classes in Phoenix, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

ACT Test Prep in Phoenix, ISEE Test Prep in Phoenix, LSAT Test Prep in Miami, GRE Test Prep in Miami, GRE Test Prep in Dallas Fort Worth, LSAT Test Prep in Denver, SAT Test Prep in Chicago, MCAT Test Prep in Houston, LSAT Test Prep in New York City, ISEE Test Prep in Atlanta

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

SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2 : Distance Formula

Example Question #3 : Distance Formula

Example Question #4 : Distance Formula

Example Question #5 : Distance Formula

Example Question #6 : Distance Formula

Example Question #7 : Distance Formula

Example Question #8 : Distance Formula

Example Question #9 : Distance Formula

Example Question #9 : Distance Formula

Example Question #11 : Distance Formula

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: