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 #1 : How To Find Out If Lines Are Perpendicular

Line is given by $-\frac{6}{5}x+y=4$ .

Which of the following is perpendicular to ?

Possible Answers:

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

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

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

$\frac{6}{5}x+y=3$

$\frac{3}{5}x+y=-2$

Correct answer:

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

Explanation:

Putting the equation of the line into slope-intercept form, we get

$y=\frac{6}{5}x+4$

The slope of line , therefore, is $\frac{6}{5}$ .

In order for a line to be perpendicular to the given line, it must have a slope that is the negative reciprocal of line g's slope.

The slope of any given line perpendicular to line g must be $-\frac{5}{6}$ when written in slope-intercept form. In other words, the equation of the perpendicular line must be $y=-\frac{5}{6}x +k$ where k is any constant.

Written in standard form, the equation of this perpendicular line must be $\frac{5}{6}x+y=k.$

Therefore, the most appropriate answer is $\frac{5}{6}x+y=6.$

Report an Error

Example Question #2 : How To Find Out If Lines Are Perpendicular

Given: Lines A, B, and C on the coordinate plane, as follows:

The equation of Line A is y = 3x+ 17 .

The equation of Line B is -9x + 3y =17 .

The equation of Line is 6x - 2y = 17 .

Which of the following is a true statement?

Possible Answers:

Line A and Line C are perpendicular to each other, but Line B is perpendicular to neither Line A nor Line C.

None of the statements in the other choices is true.

Line A and Line B are perpendicular to each other, but Line C is perpendicular to neither Line A nor Line B.

No two of Line A, Line B, and Line C are perpendicular to each other.

Line B and Line C are perpendicular to each other, but Line A is perpendicular to neither Line B nor Line C.

Correct answer:

No two of Line A, Line B, and Line C are perpendicular to each other.

Explanation:

Two lines are perpendicular if and only if the product of their slopes is . Therefore, we need to find the slopes of all three lines.Rewrite the equation for each line in its slope-intercept form y = mx+ b , where is the slope of the line.

Line A:

y = 3x+ 17 is already in this form. The slope of Line A is the coefficient of , which is 3.

Line B:

-9x + 3y =17

Isolate by working the same operations on both sides:

-9x + 3y + 9x =17 + 9x

3y = 9x + 17

$\frac{1}{3} \cdot 3y =\frac{1}{3} \cdot ( 9x + 17)$

$y =\frac{1}{3} \cdot 9x +\frac{1}{3} \cdot 17$

$y =3 x +\frac{17}{3}$

The slope of Line B is the coefficient of , which is 3.

Line C:

6x - 2y = 17

6x - 2y - 6x= 17 - 6x

- 2y = - 6x + 17

$- \frac{1}{2}(- 2y) = - \frac{1}{2} (- 6x + 17)$

$y = - \frac{1}{2} (- 6x) + \left ( - \frac{1}{2} \right )(17)$

$y = 3x - \frac{17}{2}$

The slope of Line C is the coefficient of , which is 3.

All three lines have slope 3, so the product of the slopes of any two of the lines is $3 \times 3 = 9 \ne -1$ . Therefore, no two of the lines are perpendicular.

Report an Error

Example Question #1 : How To Find Out If Lines Are Perpendicular

Given: Lines A, B, and C on the coordinate plane, as follows:

The equation of Line A is 2x+ 7y = 13 .

The equation of Line B is 7x - 2y = 13 .

The equation of Line C is 2x-7y = 13 .

Which of the following is a true statement?

Possible Answers:

Line A and Line C are perpendicular to each other, but Line B is perpendicular to neither Line A nor Line C.

Line A and Line B are perpendicular to each other, but Line C is perpendicular to neither Line A nor Line B.

Line B and Line C are perpendicular to each other, but Line A is perpendicular to neither Line B nor Line C.

None of the statements in the other choices is true.

No two of Line A, Line B, and Line C are perpendicular to each other.

Correct answer:

Line A and Line B are perpendicular to each other, but Line C is perpendicular to neither Line A nor Line B.

Explanation:

Two lines are perpendicular if and only if the product of their slopes is . Therefore, we need to find the slopes of all three lines.

Rewrite the equation for each line in its slope-intercept form y = mx+ b , where is the slope of the line.

Line A:

2x+ 7y = 13

Isolate by working the same operations on both sides:

2x+ 7y - 2x = 13 - 2x

7y = - 2x+ 13

$\frac{1}{7} \cdot 7y = \frac{1}{7} \cdot ( - 2x+ 13)$

$y = \frac{1}{7} \cdot ( - 2x) +\frac{1}{7} \cdot 13$

$y = - \frac{2}{7} x +\frac{13}{7}$

The slope of Line A is the coefficient of , which is $- \frac{2}{7}$ .

Take the same steps with the equations of the other two lines:

Line B:

7x - 2y = 13

7x - 2y -7x = 13-7x

- 2y = -7x + 13

$- \frac{1}{2}(- 2y) =- \frac{1}{2}( -7x + 13)$

$y = - \frac{1}{2}( -7x) +\left ( - \frac{1}{2} \right ) ( 13)$

$y = \frac{7}{2} x - \frac{13}{2}$

The slope of Line B is $\frac{7}{2}$

Line C:

2x-7y = 13

2x-7y - 2x = 13 - 2x

-7y = - 2x + 13

$-\frac{1}{7}(-7y) = -\frac{1}{7} (- 2x + 13)$

$y = -\frac{1}{7} (- 2x ) + \left ( -\frac{1}{7} \right )(13)$

$y = \frac{2}{7} x -\frac{13}{7}$

The slope of Line C is $\frac{2}{7}$ .

The product of the slopes of Lines A and B is $- \frac{2}{7} \times \frac{7}{2} = -1$ , so these two lines are perpendicular.

The product of the slopes of Lines A and C is $- \frac{2}{7} \times \frac{2}{7} = -\frac{4}{49}$ , so these two lines are not perpendicular.

The product of the slopes of Lines B and C is $\frac{7}{2} \times \frac{2}{7}= 1$ , so these two lines are not perpendicular.

Report an Error

Example Question #7 : How To Find Out If Lines Are Perpendicular

Given: Lines A, B, and C on the coordinate plane, as follows:

Line A has intercepts (0,4) and (6,0 ) .

Line B has intercepts (0, -6) and (9, 0) .

Line C has intercepts (0,- 8 ) and (-12, 0 ) .

Which of the following statements is true?

Possible Answers:

No two of Line A, Line B, and Line C are perpendicular to each other.

Line A and Line B are perpendicular to each other, but Line C is perpendicular to neither Line A nor Line B.

Line B and Line C are perpendicular to each other, but Line A is perpendicular to neither Line B nor Line C.

Line A and Line C are perpendicular to each other, but Line B is perpendicular to neither Line A nor Line C.

None of the statements in the other choices is true.

Correct answer:

No two of Line A, Line B, and Line C are perpendicular to each other.

Explanation:

The slope of each line, given the coordinates of two points through which they pass, can be calculated by substituting the point coordinates into the slope formula

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

Line A:

Setting $y_{1} = x_{2}= 0, x_{1} = 6 , y_{2} = 4$ and substituting:

$m = \frac{4-0}{0- 6} = \frac{4}{-6} = -\frac{2}{3}$

Line B:

Setting $y_{1} = x_{2}= 0, x_{1} = 9 , y_{2} = -6$ and substituting:

$m = \frac{-6-0}{0- 9} = \frac{-6}{-9} = \frac{2}{3}$

Line C:

Setting $y_{1} = x_{2}= 0, x_{1} = -12 , y_{2} = -8$ and substituting:

$m = \frac{-8-0}{0- (-12)} = \frac{-8}{12} = -\frac{2}{3}$

The product of the slopes of Line A and Line B is $- \frac{2}{3} \times \frac{2}{3} = -\frac{4}{9}$ , as is the product of the slopes of Line C and Line B; Since neither product is equal to , neither pair of lines is perpendicular. Also, the slopes of Line A and Line C are equal, so the lines are parallel, not perpendicular.

Report an Error

Example Question #1 : Perpendicular Lines

Which of the following lines is perpendicular to $y=3x-4$

Possible Answers:

$y=-3x-4$

$y=-\frac{1}{3}x-4$

$y=\frac{1}{3}x-4$

$y=\frac{1}{3}x+4$

Correct answer:

$y=-\frac{1}{3}x-4$

Explanation:

The line which is perpendicular has a slope which is the negative inverse of the slope of the original line.

Report an Error

Example Question #81 : Lines

Trans

Lines P and Q are parallel. Find the value of .

Possible Answers:

$x=5 + \sqrt{ 205}$

$x=-5+ \sqrt{ 205}$

$x= \sqrt{ 205}$

$x=\pm \sqrt{ 205}$

$x=-5- \sqrt{ 205}$

Correct answer:

$x=-5+ \sqrt{ 205}$

Explanation:

Since these are complementary angles, we can set up the following equation.

x^2+4+10x-4=180

x^2+10x=180

x^2+10x-180=0

Now we will use the quadratic formula to solve for .

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-10\pm \sqrt{10^2-4(1)(-180)}}{2(1)}$

$x=\frac{-10\pm \sqrt{100+720}}{2}$

$x=\frac{-10\pm \sqrt{820}}{2}$

$x=\frac{-10\pm \sqrt{4\cdot 205}}{2}$

$x=\frac{-10\pm 2\sqrt{ 205}}{2}$

$x=-5\pm \sqrt{ 205}$

Note, however, that the measure of an angle cannot be negative, so $x=-5- \sqrt{ 205}$ is not a viable answer. The correct answer, then, is $x=-5+ \sqrt{ 205}$

Report an Error

Example Question #1 : Other Lines

In the xy -plane, line l is given by the equation 2x - 3y = 5. If line l passes through the point (a ,1), what is the value of a ?

Possible Answers:

-2

-1

Correct answer: 4

Explanation:

The equation of line l relates x -values and y -values that lie along the line. The question is asking for the x -value of a point on the line whose y -value is 1, so we are looking for the x -value on the line when the y-value is 1. In the equation of the line, plug 1 in for y and solve for x:

2x - 3(1) = 5

2x - 3 = 5

2x = 8

x = 4. So the missing x-value on line l is 4.

Report an Error

Example Question #2 : Other Lines

The equation of a line is: 2x + 9y = 71

Which of these points is on that line?

Possible Answers:

(2,7)

(-2,7)

(4,7)

(4,-7)

(-4,7)

Correct answer:

(4,7)

Explanation:

Test the difference combinations out starting with the most repeated number. In this case, y = 7 appears most often in the answers. Plug in y=7 and solve for x. If the answer does not appear on the list, solve for the next most common coordinate.

2(x) + 9(7) = 71

2x + 63 = 71

2x = 8

x = 4

Therefore the answer is (4, 7)

Report an Error

Example Question #3 : Points And Distance Formula

Which of the following lines contains the point (8, 9)?

Possible Answers:

$\dpi{100} \small 8x=9y$

$\dpi{100} \small 3x+6=y$

$\dpi{100} \small 3x-6=2y$

$\dpi{100} \small 8x+9=y$

$\dpi{100} \small 3x+6=2y$

Correct answer:

$\dpi{100} \small 3x-6=2y$

Explanation:

In order to find out which of these lines is correct, we simply plug in the values $\dpi{100} \small x=8$ and $\dpi{100} \small y=9$ into each equation and see if it balances.

The only one for which this will work is $\dpi{100} \small 3x-6=2y$

Report an Error

Example Question #471 : Geometry

$\dpi{100} \small 5x+25y = 125$

Which point lies on this line?

Possible Answers:

$\dpi{100} \small (1,4)$

$\dpi{100} \small (1,5)$

$\dpi{100} \small (5,4)$

$\dpi{100} \small (5,1)$

$\dpi{100} \small (5,5)$

Correct answer:

$\dpi{100} \small (5,4)$

Explanation:

$\dpi{100} \small 5x+25y = 125$

Test the coordinates to find the ordered pair that makes the equation of the line true:

$\dpi{100} \small (5,4)$

$\dpi{100} \small 5 (5) + 25 (4) = 25 + 100 = 125$

$\dpi{100} \small (1,5)$

$\dpi{100} \small 5(1)+25(5)= 5+125=130$

$\dpi{100} \small (5,1)$

$\dpi{100} \small 5(5)+25(1)= 25+25=50$

$\dpi{100} \small (5,5)$

$\dpi{100} \small 5(5)+25(5)= 25+125=150$

$\dpi{100} \small (1,4)$

$\dpi{100} \small 5(1)+25(4)= 5+100=105$

Report an Error

View SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Irina
Certified Tutor

New York University, Bachelors, Biochemistry.

View SAT Mathematics Tutors

Stephen
Certified Tutor

Grinnell College, Bachelor in Arts, Computer Science.

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

ACT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Phoenix, Spanish Courses & Classes in Miami, SAT Courses & Classes in Boston, ACT Courses & Classes in Los Angeles, ACT Courses & Classes in Washington DC, MCAT Courses & Classes in Boston, GRE Courses & Classes in Houston, GRE Courses & Classes in Seattle, ISEE Courses & Classes in Philadelphia

Popular Test Prep

ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in San Diego, ACT Test Prep in Washington DC, ACT Test Prep in Los Angeles, ISEE Test Prep in Seattle, MCAT Test Prep in Houston, MCAT Test Prep in New York City, MCAT Test Prep in Washington DC, MCAT Test Prep in Chicago, GRE Test Prep in Houston

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 #1 : How To Find Out If Lines Are Perpendicular

Example Question #2 : How To Find Out If Lines Are Perpendicular

Example Question #1 : How To Find Out If Lines Are Perpendicular

Example Question #7 : How To Find Out If Lines Are Perpendicular

Example Question #1 : Perpendicular Lines

Example Question #81 : Lines

Example Question #1 : Other Lines

Example Question #2 : Other Lines

Example Question #3 : Points And Distance Formula

Example Question #471 : Geometry

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: