Question

figure a is a scale drawing of an original figure. it was produced by using a scale factor of $\frac{3}{5}$. modify figure b so that the scale factor from the original figure to figure b is $\frac{1}{5}$.

Explanation:

Step1: Find the relationship between the scale - factors

Let the scale - factor from the original figure to Figure A be $k_A=\frac{3}{5}$, and the desired scale - factor from the original figure to Figure B be $k_B = \frac{1}{5}$. We want to find the factor by which we need to scale Figure B relative to Figure A. Let this factor be $x$. Then $k_B=k_A\times x$. So, $x=\frac{k_B}{k_A}$.

Step2: Calculate the scaling factor $x$

Substitute $k_A = \frac{3}{5}$ and $k_B=\frac{1}{5}$ into the formula $x=\frac{k_B}{k_A}$. We get $x=\frac{\frac{1}{5}}{\frac{3}{5}}=\frac{1}{5}\times\frac{5}{3}=\frac{1}{3}$.

Step3: Modify Figure B

To modify Figure B so that the scale - factor from the original figure to Figure B is $\frac{1}{5}$, we need to scale each side - length of Figure B by a factor of $\frac{1}{3}$. For example, if a side - length of Figure B is $l$, the new side - length $l'$ after scaling is $l'=\frac{1}{3}l$.

Answer:

Scale each side - length of Figure B by a factor of $\frac{1}{3}$.