Unit A: Geometry

Chapter 2: Transformations

Practice

Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You will learn the material more thoroughly if you complete the questions before checking the answers.

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Practice
Solutions

Quadrilateral ABCD is similar to quadrilateral EFGH.

List all corresponding side lengths.

What scale factor was applied to quadrilateral ABCD to create quadrilateral EFGH?

Julie purchased a hot tub with dimensions of 5 ft by 8 ft.

Julie would like to build a deck that is similar to the hot tub and has a width of 13.5 ft. What length must the deck be?

Question 1

Quadrilateral ABCD is similar to quadrilateral EFGH.

List all corresponding side lengths.

What scale factor was applied to quadrilateral ABCD to create quadrilateral EFGH?

Solutions

AB corresponds to GH
BC corresponds to HE
CD corresponds to EF
AD corresponds to GF

Scale Factor = \frac{Dimension of Image}{Dimension of Original}

\begin{array}{rcl} \frac{G H}{A B} & = & \frac{10.5}{35} \\ = & 0.3 \end{array}

\begin{array}{rcl} \frac{H E}{B C} & = & \frac{11.1}{37} \\ = & 0.3 \end{array}

\begin{array}{rcl} \frac{E F}{C D} & = & \frac{12}{40} \\ = & 0.3 \end{array}

\begin{array}{rcl} \frac{G F}{A D} & = & \frac{17.4}{58} \\ = & 0.3 \end{array}

Each side in quadrilateral ABCD was multiplied by the scale factor of 0.3 to create quadrilateral EFGH.

It is necessary that the scale factor is calculated for more than one dimension to ensure that the polygons are similar.

Question 2

Julie purchased a hot tub with dimensions of 5 ft by 8 ft.

Julie would like to build a deck that is similar to the hot tub and has a width of 13.5 ft. What length must the deck be?

Solution

Step 1: Find the scale factor. The new side of 13.5 ft corresponds to the original side of 5 ft.

\begin{array}{rcl} Scale Factor & = & \frac{Dimensions of Image}{Dimensions of Original} \\ = & \frac{13.5}{5} \\ = & 2.7 \end{array}

Step 2: Find the length of the deck. To find the length, multiply the length of the hot tub by the scale factor.

\begin{array}{rcl} L & = & 8 ft \times 2.7 \\ = & 21.6 ft \end{array}

The length of the deck must be 21.6 ft.