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 type of scale - drawing A

Since scale - drawing A is smaller than the original figure, it is a reduction.

Step2: Find scale factor of A

If we assume the scale factor is $k_A$, and since it is a reduction, if we consider a length relationship, say the length of a side of the original is $l$ and of scale - drawing A is $l_A$, and if $l_A=\frac{1}{2}l$, the scale factor $k_A = \frac{1}{2}$.

Step3: Determine type of scale - drawing B

Since scale - drawing B is larger than the original figure, it is an enlargement.

Step4: Find scale factor of B

If the length of a side of the original is $l$ and of scale - drawing B is $l_B$, and $l_B = 2l$, the scale factor $k_B=2$.

Step5: Find equation relating A and B

We know that the scale factor from A to B is the ratio of the scale factor of B to the scale factor of A. Since $k_B = 2$ and $k_A=\frac{1}{2}$, if $b$ is a length in B and $a$ is a length in A, then $b = 4a$.

Answer:

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