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

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Example Question #1535 :Plane Geometry

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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 arenoton the same line. As seen below, points,, andare on the same line.

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Therefore, Planeis not a valid name for the plane.

Example Question #1543 :Basic Geometry

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Refer to the above figure.

True or false:andcomprise a pair of opposite rays.

Possible Answers:

True

False

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.andboth have endpoint, so the first criterion is met.passes through pointandpasses through point;andare 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 #3 :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 lineis indicated in green below.

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

Example Question #1587 :Basic Geometry

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Refer to the above diagram.

True or false:andcomprise a pair of vertical angles.

Possible Answers:

True

False

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,andare marked in green and red, respectively:

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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 #1590 :Basic Geometry

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Refer to the above diagram.

True or false:andcomprise a linear pair.

Possible Answers:

True

False

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,andare 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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