Question

1. use the diagram to answer parts (a)-(e). a. is scale drawing a an enlargement or a reduction of the original figure? b. what is the scale factor that relates scale drawing a to the original figure? c. is scale drawing b an enlargement or a reduction of the original figure? d. what is the scale factor that relates scale drawing b to the original figure? e. write an equation that relates the lengths of scale drawing b to the lengths of scale drawing a. let b represent a length of scale drawing b, and let a represent the corresponding length of scale drawing a.

Explanation:

Step1: Determine reduction/enlargement for A

Compare size of A to original. Since A is smaller, it's a reduction.

Step2: Find scale - factor for A

Count grid - units. Suppose original length is 4 units and A length is 2 units. Scale factor $k_A=\frac{2}{4}=\frac{1}{2}$.

Step3: Determine reduction/enlargement for B

Compare size of B to original. Since B is larger, it's an enlargement.

Step4: Find scale - factor for B

Suppose original length is 4 units and B length is 8 units. Scale factor $k_B = \frac{8}{4}=2$.

Step5: Find relation between A and B

We know $k_A=\frac{1}{2}$ and $k_B = 2$. If $a$ is length in A and $b$ is length in B, and original length is $x$, then $a=\frac{1}{2}x$ and $b = 2x$. So $b=4a$.

Answer:

a. Reduction
b. $\frac{1}{2}$
c. Enlargement
d. 2
e. $b = 4a$