Question

1. in the figures shown, △def is a scale drawing of △abc.

a. is △def an enlargement or a reduction of △abc?
b. what is the length of the side of △def that corresponds to side ab in △abc?
c. determine the scale factor that relates △def to △abc.

1. rectangle efgh is a scale drawing of rectangle abcd. determine the scale factor, and state whether it is an enlargement or a reduction.

Explanation:

Step1: Analyze side - lengths for triangle

Compare side - lengths of $\triangle ABC$ and $\triangle DEF$. Sides of $\triangle ABC$ are 6, 9, 12 and sides of $\triangle DEF$ are $1\frac{1}{2}$, $2\frac{1}{4}$, 3. Since the side - lengths of $\triangle DEF$ are smaller, it is a reduction.

Step2: Identify corresponding side

The side of $\triangle ABC$ is $AB = 12$, and the corresponding side of $\triangle DEF$ is $DE=3$.

Step3: Calculate scale factor for triangle

The scale factor $k$ from $\triangle ABC$ to $\triangle DEF$ is found by dividing the length of a side of $\triangle DEF$ by the length of the corresponding side of $\triangle ABC$. Using $AB$ and $DE$, $k=\frac{DE}{AB}=\frac{3}{12}=\frac{1}{4}$.

Step4: Analyze side - lengths for rectangles

For rectangles, side of rectangle $ABCD$ has length $AD = 2\frac{1}{4}$ and corresponding side of rectangle $EFGH$ has length $EH = 1\frac{1}{2}$, and side of rectangle $ABCD$ has length $AB = 6$ and corresponding side of rectangle $EFGH$ has length $EF = 4$. Since the side - lengths of $EFGH$ are smaller, it is a reduction.

Step5: Calculate scale factor for rectangles

Using the length of $AB$ and $EF$, the scale factor $k=\frac{EF}{AB}=\frac{4}{6}=\frac{2}{3}$. Using the length of $AD$ and $EH$, $k=\frac{EH}{AD}=\frac{1\frac{1}{2}}{2\frac{1}{4}}=\frac{\frac{3}{2}}{\frac{9}{4}}=\frac{3}{2}\times\frac{4}{9}=\frac{2}{3}$.

Answer:

a. Reduction
b. 3
c. $\frac{1}{4}$

1. Scale factor: $\frac{2}{3}$, Reduction