Question

figure a is a scale drawing of an original figure. it was produced by using a scale factor of $\frac{2}{5}$. modify figure b so that the scale factor from the original figure to figure b is $\frac{3}{5}$

Explanation:

Step1: Find the relationship between scale - factors

Let the scale - factor from the original figure to Figure A be $k_A=\frac{2}{5}$, and the desired scale - factor from the original figure to Figure B be $k_B = \frac{3}{5}$. We want to find the scale - factor $k$ from Figure A to Figure B. Using the property of scale - factors $k_B=k\times k_A$, so $k=\frac{k_B}{k_A}$.

Step2: Calculate the scale - factor from Figure A to Figure B

Substitute $k_A=\frac{2}{5}$ and $k_B=\frac{3}{5}$ into the formula $k = \frac{k_B}{k_A}$. Then $k=\frac{\frac{3}{5}}{\frac{2}{5}}=\frac{3}{2}$.

Step3: Modify the dimensions of Figure B

To modify Figure B, we multiply the coordinates of each vertex of Figure B by the scale - factor $\frac{3}{2}$. For example, if a vertex of Figure B has coordinates $(x,y)$, the new coordinates $(x',y')$ after modification will be $x'=\frac{3}{2}x$ and $y'=\frac{3}{2}y$. In terms of the grid - based figure, if a side - length of Figure B is $l$ (in grid units), the new side - length will be $\frac{3}{2}l$ grid units.

Answer:

Multiply the dimensions of each part of Figure B by $\frac{3}{2}$ (or increase the side - lengths and distances between vertices of Figure B by a factor of $\frac{3}{2}$).