SAT Math : How to find transformation for an analytic geometry equation

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Find A Ray

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Refer to the above diagram. The plane containing the above figure can be called Plane .

Possible Answers:

True

False

Correct answer:

False

Explanation:

A plane can be named after any three points on the plane that are not on the same line. As seen below, points ,  and  are on the same line. 

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Therefore, Plane  is not a valid name for the plane.

Example Question #1541 : Basic Geometry

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Refer to the above figure. 

True or false:  and  comprise a pair of opposite rays.

Possible Answers:

False

True

Correct answer:

True

Explanation:

 

Two rays are opposite rays, by definition, if 

(1) they have the same endpoint, and

(2) their union is a line.

The first letter in the name of a ray refers to its endpoint; the second refers to the name of any other point on the ray.  and  both have endpoint , so the first criterion is met.  passes through point  and  passes through point  and  are indicated below in green and red, respectively:

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The union of the two rays is a line. Both criteria are met, so the rays are indeed opposite.

Example Question #1 : New Sat Math Calculator

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Refer to the above diagram:

True or false:  may also called .

Possible Answers:

True

False

Correct answer:

False

Explanation:

A line can be named after any two points it passes through. The line  is indicated in green below.

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The line does not pass through , so  cannot be part of the name of the line. Specifically,  is not a valid name.

Example Question #33 : How To Find An Angle Of A Line

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Refer to the above diagram.

True or false:  and  comprise a pair of vertical angles.

Possible Answers:

False

True

Correct answer:

False

Explanation:

By definition, two angles comprise a pair of vertical angles if 

(1) they have the same vertex; and

(2) the union of the two angles is exactly a pair of intersecting lines.

In the figure below,  and  are marked in green and red, respectively:

Lines 2

 

While the two angles have the same vertex, their union is not a pair of intersecting lines. The two angles are not a vertical pair.

Example Question #42 : How To Find An Angle Of A Line

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Refer to the above diagram.

True or false:  and  comprise a linear pair.

Possible Answers:

False

True

Correct answer:

False

Explanation:

By definition, two angles form a linear pair if and only if 

(1) they have the same vertex;

(2) they share a side; and,

(3) their interiors have no points in common.

In the figure below,  and  are marked in green and red, respectively:

Lines 2

The two angles have the same vertex and share no interior points. However, they do not share a side. Therefore, they do not comprise a linear pair.

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