We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : Perpendicular Lines

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 Next →

Example Question #64 : Coordinate Geometry

Screen_shot_2013-09-04_at_10.56.34_am

What is the equation of a line perpendicular to the one above, passing through the point (2,2) ?

Possible Answers:

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

$y=-\frac{1}{3}x+\frac{8}{3}$

$y=-\frac{1}{2}x+3$

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

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

Correct answer:

$y=-\frac{1}{3}x+\frac{8}{3}$

Explanation:

Looking at the graph, we can tell the slope of the line is 3 with a $\dpi{100} y$ -intercept of , so the equation of the line is:

$y=3x-4$

A perpendicular line to this would have a slope of $-\frac{1}{3}$ , and would pass through the point (2,2) so it follows:

$y=-\frac{1}{3}x+c\rightarrow 2=-\frac{1}{3}(2)+c\rightarrow c=8/3\rightarrow y=-\frac{1}{3}x+\frac{8}{3}$

Report an Error

Example Question #61 : Coordinate Geometry

Line M passes through the points (2,2) and (3,–5). Which of the following is perpendicular to line M?

Possible Answers:

y = –(1/7)x – 1

y = (1/7)x + 3

y = 7x – 6

y = –7x – 5

y = 7x + 4

Correct answer:

y = (1/7)x + 3

Explanation:

First we find the slope of line M by using the slope formula (y₂– y₁)/(x₂– x₁).

(–5 – 2)/(3 – 2) = –7/1. This means the slope of Line M is –7. A line perpendicular to Line M will have a negative reciprocal slope. Thus, the answer is y = (1/7)x + 3.

Report an Error

Example Question #66 : Coordinate Geometry

Tangent_line

Figure not drawn to scale.

In the figure above, a circle is centered at point C and a line is tangent to the circle at point B. What is the equation of the line?

Possible Answers:

2x + 5y = -1

5x + 2y = 29

2x - 5y = 29

x + y = 4

5x - 2y = 41

Correct answer:

5x + 2y = 29

Explanation:

We know that the line passes through point B, but we must calculate its slope in order to find the equation that defines the line. Because the line is tangent to the circle, it must make a right angle with the radius of the circle at point B. Therefore, the slope of the line is perpendicular to the slope of the radius that connects the center of the circle to point B. First, we can find the slope of the radius, and then we can determine the perpendicular slope.

The radius passes through points C and B. We can use the formula for the slope (represented as ) between two points to find the slope of the radius.

Point C: (2,-5) and point B: (7,-3)

$m_{rad}=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-(-5)}{7-2}$

$m_{rad}=\frac{2}{5}$

This is the slope of the radius, but we need to find the slope of the line that is perpendicular to the radius. This value will be equal to the negative reciprocal.

$m=-\frac{1}{m_{rad}}=-\frac{1}{\frac{2}{5}}=-\frac{5}{2}$

Now we know the slope of the tangent line. We can use the point-slope formula to find the equation of the line. The formula is shown below.

y-y_1=m(x-x_1)

Plug in the give point that lies on the tangent line (point B) and simplify the equation.

$y-(-3)=-\frac{5}{2}(x-7)$

Multiply both sides by two in order to remove the fraction.

2(y -(-3)) = -5(x -7)

2(y + 3) = -5(x - 7)

Distribute both sides.

2y + 6 = -5x + 35

Add to both sides.

5x + 2y + 6 = 35

Subtract six from both sides.

5x + 2y = 29

The answer is 5x + 2y = 29 .

Report an Error

Example Question #1 : How To Find The Slope Of Perpendicular Lines

Solve the equation for x and y.

x² + y = 31

x + y = 11

Possible Answers:

x = 5, –4

y = 6, 15

x = 6, 15

y = 5, –4

x = 8, –6

y = 13, 7

x = 13, 7

y = 8, –6

Correct answer:

x = 5, –4

y = 6, 15

Explanation:

Solving the equation follows the same system as the first problem. However since x is squared in this problem we will have two possible solutions for each unknown. Again substitute y=11-x and solve from there. Hence, x2+11-x=31. So x2-x=20. 5 squared is 25, minus 5 is 20. Now we know 5 is one of our solutions. Then we must solve for the second solution which is -4. -4 squared is 16 and 16 –(-4) is 20. The last step is to solve for y for the two possible solutions of x. We get 15 and 6. The graph below illustrates to solutions.

Sat_math_165_02

Report an Error

Example Question #581 : Sat Mathematics

Solve the equation for x and y.

x² – y = 96

x + y = 14

Possible Answers:

x = 5, –14

y = 15, 8

x = 25, 4

y = 10, –11

x = 15, 8

y = 5, –14

x = 10, –11

y = 25, 4

Correct answer:

x = 10, –11

y = 25, 4

Explanation:

This problem is very similar to number 2. Derive y=14-x and solve from there. The graph below illustrates the solution.

Sat_math_165_03

Report an Error

Example Question #52 : Psat Mathematics

Solve the equation for x and y.

5x² + y = 20

x² + 2y = 10

Possible Answers:

x = 14, 5

y = 4, 6

x = √4/5, 7

y = √3/10, 4

x = √10/3, –√10/3

y = 10/3

No solution

Correct answer:

x = √10/3, –√10/3

y = 10/3

Explanation:

The problem involves the same method used for the rest of the practice set. However since the x is squared we will have multiple solutions. Solve this one in the same way as number 2. However be careful to notice that the y value is the same for both x values. The graph below illustrates the solution.

Sat_math_165_06

Report an Error

Example Question #1 : How To Find The Equation Of A Curve

Solve the equation for x and y.

x² + y = 60

x – y = 50

Possible Answers:

x = –40, –61

y = 10, –11

x = 10, –11

y = –40, –61

x = 40, 61

y = 11, –10

x = 11, –10

y = 40, 61

Correct answer:

x = 10, –11

y = –40, –61

Explanation:

This is a system of equations problem with an x squared, to be solved just like the rest of the problem set. Two solutions are required due to the x2. The graph below illustrates those solutions.

Sat_math_165_10

Report an Error

Example Question #61 : Coordinate Geometry

A line passes through the points $(3,5)$ and $(4,7)$ . What is the equation for the line?

Possible Answers:

$y=\frac{1}{2}x+3.5$

$y=2x$

None of the available answers

$y=2x-1$

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

Correct answer:

$y=2x-1$

Explanation:

First we will calculate the slope as follows:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{7-5}{4-3}=\frac{2}{1}=2$

And our equation for a line is

$y=mx+b=2x+b$

Now we need to calculate b. We can pick either of the points given and solve for $\dpi{100} b$

$5=2(3)+b$

$b=-1$

Our equation for the line becomes

$y=2x-1$

Report an Error

Example Question #61 : Psat Mathematics

Axes_1

Give the slope of a line perpendicular to the line in the above figure.

Possible Answers:

$\frac{1}{2}$

None of the other responses is correct.

$-\frac{1}{2}$

Correct answer:

Explanation:

In order to move from the upper left point to the lower right point, it is necessary to move down 3 units and right six units. This is a rise of and a run of 6. The slope of a line is the ratio of rise to run, so slope of the line shown is $\frac{-3}{6} = -\frac{1}{2}$ .

A line perpendicular to this will have a slope equal to the opposite of the reciprocal of $-\frac{1}{2}$ . This is $\frac{2} {1} = 2$ .

Report an Error

Example Question #38 : Coordinate Geometry

The equation of line p is y= 1/4x +6. If line k contains the point (3,5) and is perpendicular to line p, find the equation of line k.

Possible Answers:

y = -4x + 17

y = 3x + 5

y = 4x - 17

y = 1/4x + 17

Correct answer:

y = -4x + 17

Explanation:

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.

Report an Error

← Previous 1 2 3 4 5 Next →

View PSAT Mathematics Tutors

Gregory
Certified Tutor

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

View PSAT Mathematics Tutors

Chase
Certified Tutor

University of Memphis, Bachelor in Arts, Psychology.

View PSAT Mathematics Tutors

Anubhuti
Certified Tutor

KiiT University, Bachelor of Science, Electronics Technology.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Atlanta, Math Tutors in Phoenix, SAT Tutors in Phoenix, Math Tutors in Denver, MCAT Tutors in Denver, French Tutors in Washington DC, Computer Science Tutors in Los Angeles, Chemistry Tutors in Phoenix, Math Tutors in Atlanta, GMAT Tutors in Dallas Fort Worth

Popular Courses & Classes

SSAT Courses & Classes in Seattle, GMAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Seattle, SSAT Courses & Classes in Phoenix, Spanish Courses & Classes in Phoenix, LSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in Houston, ISEE Courses & Classes in Boston

Popular Test Prep

SSAT Test Prep in Denver, GMAT Test Prep in Seattle, GMAT Test Prep in Houston, GRE Test Prep in San Francisco-Bay Area, LSAT Test Prep in San Diego, SAT Test Prep in Houston, ISEE Test Prep in Seattle, ACT Test Prep in Houston, SSAT Test Prep in New York City, MCAT 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

PSAT Math : Perpendicular Lines

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #64 : Coordinate Geometry

Example Question #61 : Coordinate Geometry

Example Question #66 : Coordinate Geometry

Example Question #1 : How To Find The Slope Of Perpendicular Lines

Example Question #581 : Sat Mathematics

Example Question #52 : Psat Mathematics

Example Question #1 : How To Find The Equation Of A Curve

Example Question #61 : Coordinate Geometry

Example Question #61 : Psat Mathematics

Example Question #38 : Coordinate Geometry

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: