We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math II : Coordinate Geometry

Study concepts, example questions & explanations for SAT II Math II

Create An Account

All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #11 : Coordinate Geometry

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

$g(x) =\left | \frac{1}{4}x \right |- 4$

$g(x) =\left | \frac{1}{4}x+1 \right |$

g(x) =-|4x |- 4

g(x) =-|4x+16|

$g(x) =\left | \frac{1}{4}x-1 \right |$

Correct answer:

$g(x) =\left | \frac{1}{4}x \right |- 4$

Explanation:

Below is the graph of f(x) = |x| :

Axes_1

If the graph of is translated by shifting each point (x,y) to the point $\left ( x, \frac{1}{4}y \right )$ , the graph of

$g(x) = \frac{1}{4}f(x)$

is formed. If the graph is then shifted down by four units, the new graph is

$g(x) = \frac{1}{4}f(x)- 4$ .

Since the starting graph was f(x) = |x| , the final graph is

$g(x) = \frac{1}{4}|x|- 4$ , or

$g(x) =\left | \frac{1}{4}x \right |- 4$

Report an Error

Example Question #12 : Coordinate Geometry

Axes_1

Refer to the above figure.

Which of the following functions is graphed?

Possible Answers:

g(x) = |3x-6|

$g(x) =\left | \frac{1}{3} x \right |+2$

g(x) = |3x|-2

$g(x) =\left | \frac{1}{3} x+ \frac{2}{3} \right |$

$g(x) =\left | \frac{1}{3} x- \frac{2}{3} \right |$

Correct answer:

$g(x) =\left | \frac{1}{3} x- \frac{2}{3} \right |$

Explanation:

Below is the graph of f(x) = |x| :

Axes_1

If the graph of is translated by shifting each point (x,y) to the point $\left ( x, \frac{1}{3}y \right )$ , the graph of

$g(x) = \frac{1}{3}f(x)$

is formed. If the graph is then shifted right by two units, the new graph is

$g(x) = \frac{1}{3}f(x-2)$

Since the starting graph was f(x) = |x| , the final graph is

$g(x) = \frac{1}{3} |x-2|$ , or

$g(x) =\left | \frac{1}{3} x- \frac{2}{3} \right |$

Report an Error

Example Question #1 : Distance Formula

What is the distance between the point (1,2) and (8,5)?

Possible Answers:

13.9

$\sqrt58$

Correct answer:

$\sqrt58$

Explanation:

For this question we will use the distance formula to solve.

$d=\sqrt((x_2-x_1)^2+(y_2-y_1)^2)$

In our case (x_1, y_1)=(1,2)

and (x_2, y_2)= (8,5)

Substituting these values in we get the following

$d=\sqrt((8-1)^2+(5-2)^2)$

$d=\sqrt(7^2+3^2)$

$d=\sqrt(49+9)$

$d=\sqrt(58)$

Report an Error

Example Question #1 : Distance Formula

The points A=(-2,0), B=(0,3), and C=(0,0) makes a triangle. What is the distance between point A and point B?

Possible Answers:

$\sqrt15$

$\sqrt13$

Correct answer:

$\sqrt13$

Explanation:

For this question we need to use the distance formula for points A and B.

Point A will be our (x_1, y_1) and point B will be (x_2, y_2)

Now we substitute these values into the following:

$d=\sqrt((0--2)^2+(3-0)^2)$

$d=\sqrt(2^2+3^2)$

$d=\sqrt(4+9)$

$d=\sqrt13$

Report an Error

Example Question #11 : Coordinate Geometry

Find the distance between the two points (2,7) and (4,6).

Possible Answers:

$\sqrt{17}$

$\sqrt{3}$

$\sqrt{5}$

$\sqrt{205}$

Correct answer:

$\sqrt{5}$

Explanation:

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

For this problem the values are as follows:

$x_{1}=2$

$x_{2}=4$

$y_{1}=7$

$y_{2}=6$

Input the values into the formula and simplify

$d=\sqrt{(4-2)^2+(7-6)^2}=\sqrt{(2)^2+(1)^2}=\sqrt{4+1}=\sqrt{5}$

Report an Error

Example Question #16 : Coordinate Geometry

Find the point halfway between points A and B.

A=(19,54)

B=(67,34)

Possible Answers:

(86,88)

(43,44)

(42,45)

(44,43)

Correct answer:

(43,44)

Explanation:

Find the point halfway between points A and B.

A=(19,54)

B=(67,34)

We are going to need to use midpoint formula. If you ever have difficulty recalling midpoint formula, try to recall that it is basically taking two averages. One average is the average of your x values, the other average is the average of your y values.

$Mid=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Now we plug and chug!

$Mid=(\frac{19+67}{2},\frac{54+34}{2})=(\frac{86}{2},\frac{88}{2})=(43,44)$

So our answer is (43,44)

Report an Error

Example Question #1 : Midpoint Formula

What is the coordinates of the point exactly half way between (-2, -3) and (5, 7)?

Possible Answers:

(3,-2)

$\left(\frac{3}{2}, 2\right)$

$\left(2, \frac{-3}{2}\right)$

(2, -3)

Correct answer:

$\left(\frac{3}{2}, 2\right)$

Explanation:

We need to use the midpoint formula to solve this question.

$midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In our case (x_1, y_1)=(-2,-3)

and (x_2, y_2)=(5,7)

Therefore, substituting these values in we get the following:

$midpoint=(\frac{-2+5}{2}, \frac{-3+7}{2})$

$midpoint= (\frac{3}{2}, \frac{4}{2})$

$(\frac{3}{2}, 2)$

Report an Error

Example Question #1 : Midpoint Formula

Find the midpoint between (2,3) and (-1,9) .

Possible Answers:

$(\frac{1}{2}, -3)$

$(\frac{1}{2}, 6)$

$(\frac{3}{2}, 3)$

$(\frac{3}{2}, -3)$

$(\frac{1}{2}, -6)$

Correct answer:

$(\frac{1}{2}, 6)$

Explanation:

Write the midpoint formula.

$M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Substitute the points.

$M = (\frac{2+(-1)}{2}, \frac{3+9}{2}) = (\frac{1}{2}, 6)$

The answer is: $(\frac{1}{2}, 6)$

Report an Error

Example Question #1 : Other Coordinate Geometry

On the coordinate plane, two lines intersect at the origin. One line passes through the point (3, 2) ; the other, (3, 4) .

Give the measures of the acute angles they form at their intersection (nearest degree).

Possible Answers:

$71^{\circ }$

$21^{\circ }$

$69^{\circ }$

$19 ^{\circ }$

$34 ^{\circ }$

Correct answer:

$19 ^{\circ }$

Explanation:

If $\theta$ is the measure of the angles that two lines with slopes $m_{1}$ and $m_{2}$ form, then

$\tan \theta = \frac{m_{1}-m _{2}}{1+m_{1}m_{2}}$ ,

The slopes of the lines can be found by applying the slope formula

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

using the known points.

For the first line, set $x_{1}= y_{1} = 0, x_{2}= 3, y_{2} = 4$ :

$m_{1} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{4-0}{3-0} = \frac{4}{3}$

The inverse tangent of this is

$\tan^{-1} \frac{4}{3} \approx 53.1^{\circ }$ ,

making this the angle this line forms with the -axis.

For the second line, set $x_{1}= y_{1} = 0, x_{2}= 3, y_{2} = 2$ :

$m_{2} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{2-0}{3-0} = \frac{2}{3}$

The inverse tangent of this is

$\tan^{-1} \frac{2}{3} \approx 33.7^{\circ }$

making this the angle this line forms with the -axis.

Subtract:

Taking the inverse tangent:

$\theta \approx 53.1^{\circ } - 33.7^{\circ } \approx 19.4 ^{\circ }$ .

Rounding to the nearest degree, this is $19 ^{\circ }$ .

Report an Error

Example Question #1 : Other Coordinate Geometry

In the figure below, regular hexagon ABCDEF has a side length of . Find the y-coordinate of point .

Possible Answers:

3.38

3.46

4.09

3.99

Correct answer:

3.46

Explanation:

From the given information, we know that the coordinate for must be (0, 8) .

Recall that the interior angle of a regular hexagon is $120^{\circ}$ . Thus, we can draw in the following 30-60-90 triangle.

Since we know that this is a 30-60-90 triangle, we know that the sides must be as marked, in the ratio of $1:\sqrt3:2$ . Thus, the y-coordinate of must be 3.46 .

Report an Error

← Previous 1 2 Next →

View SAT Subject Test in Mathematics Level 2 Tutors

Luu Chi Hieu
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Computer Science.

View SAT Subject Test in Mathematics Level 2 Tutors

Antonia
Certified Tutor

University of Michigan-Ann Arbor, Bachelor of Engineering, Nuclear Engineering. University of Wisconsin-Madison, Current Grad...

View SAT Subject Test in Mathematics Level 2 Tutors

Reuben
Certified Tutor

University of Alberta, Bachelor of Science, Mathematics.

All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in New York City, GRE Tutors in New York City, ISEE Tutors in Atlanta, SAT Tutors in Houston, French Tutors in Atlanta, SSAT Tutors in Philadelphia, LSAT Tutors in San Francisco-Bay Area, Reading Tutors in New York City, SSAT Tutors in Washington DC, ISEE Tutors in San Diego

Popular Courses & Classes

Spanish Courses & Classes in Miami, MCAT Courses & Classes in San Diego, ISEE Courses & Classes in Seattle, MCAT Courses & Classes in Denver, LSAT Courses & Classes in Phoenix, ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Philadelphia, GMAT Courses & Classes in New York City, GMAT Courses & Classes in Washington DC, Spanish Courses & Classes in Chicago

Popular Test Prep

MCAT Test Prep in Philadelphia, SAT Test Prep in Denver, GRE Test Prep in Los Angeles, ISEE Test Prep in Philadelphia, GMAT Test Prep in Chicago, LSAT Test Prep in New York City, SSAT Test Prep in Miami, MCAT Test Prep in Miami, MCAT Test Prep in Denver, SSAT Test Prep in Philadelphia

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 II Math II : Coordinate Geometry

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #11 : Coordinate Geometry

Example Question #12 : Coordinate Geometry

Example Question #1 : Distance Formula

Example Question #1 : Distance Formula

Example Question #11 : Coordinate Geometry

Example Question #16 : Coordinate Geometry

Example Question #1 : Midpoint Formula

Example Question #1 : Midpoint Formula

Example Question #1 : Other Coordinate Geometry

Example Question #1 : Other Coordinate Geometry

All SAT II Math II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: