Prentice Hall Geometry

Chapter 9 Transformations > 9 Cumulative Test Prep

9 Cumulative Test Prep

Tips for Success

Some problems ask you to perform a transformation on a figure in the coordinate plane. Read the sample question below. Then follow the tips to answer it.

Tip 1

To calculate the scale factor of a dilation, you need to know the lengths of a pair of corresponding sides. You are given H ′ K ′ . cap h prime , cap k prime , . You can use the graph to find HK.

Δ G ′ H ′ K ′ cap delta , g prime , h prime , k prime is the image of cap delta g h k for a dilation with center (0, 0) and H ′ K ′ = 8 . h prime , k prime , equals 8 . What are the coordinates of h prime , question mark

A graph of triangle GHK has vertices G(negative 5, negative 5), H(negative 1, 2), and K(negative 5, 2).

open negative 2 comma 4 close
( − 1 , − 2 ) open negative 1 comma negative 2 close
(1, 2)
(4, 2)

Think It Through

The scale factor is H ′ K ′ H K = 8 4 = 2 . fraction h prime , k prime , over h k end fraction . equals , 8 fourths , equals 2 .

To find the coordinates of h prime , comma multiply the coordinates of H by the scale factor. h prime is at ( 2 · ( − 1 ) , 2 · 2 ) , or ( − 2 , 4 ) . open 2 middle dot open negative 1 close comma 2 middle dot 2 close comma or open negative 2 comma 4 close . The correct answer is A.

Vocabulary Builder

As you solve problems, you must understand the meanings of mathematical terms. Match each term with its mathematical meaning.

centroid
circumcenter
line symmetry
point symmetry
proportion
tessellation

a reflection for which the figure is its own image
the point of concurrency of the medians in a triangle
an equation that states that two ratios are equal
a repeating pattern of figures that completely covers a plane, without gaps or overlaps
a symmetry for which the figure is its own image for a 180 degrees rotation
the point of concurrency of the perpendicular bisectors of a triangle

Multiple Choice

Read each question. Then write the letter of the correct answer on your paper.

Which quadrilateral must have congruent diagonals?
1. kite
2. rectangle
3. parallelogram
4. rhombus
In a 30 ° - 60 ° - 90 ° 30 degrees minus 60 degrees minus 90 degrees triangle, the shortest leg measures 13 in. What is the measure of the longer leg?
1. 13 in.
2. 13 2 in . 13 square root of 2 , in .
3. 13 3 in . 13 square root of 3 , in .
4. 26 in.
Three vertices of ▱ white parallelogram ABCD are A(1, 7), B(0, 0), and A ( 7 , − 1 ) . eh open 7 comma negative 1 close . What are the coordinates of D?
1. (6, 6)
2. (6, 8)
3. (7, 7)
4. (8, 6)

End ofPage 608

9 Cumulative Test Prep

Tips for Success

Tip 1

Tip 2

Think It Through

Multiple Choice

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