Question

given △abc with $overline{ab}$ contained in the line $2x + 3y = 5$. if △abc is dilated to get △abc, which of the following lines could contain $overline{ab}$? $2x - 3y = 10$ $3x + 2y = 10$ $2x + 3y = 10$ $3x - 2y = 10$

Explanation:

Step1: Recall dilation property

Dilation of a figure results in parallel - corresponding lines. Parallel lines have the same slope.

Step2: Find the slope of the given line

Rewrite the line $2x + 3y=5$ in slope - intercept form $y=mx + b$ (where $m$ is the slope). We get $3y=-2x + 5$, so $y=-\frac{2}{3}x+\frac{5}{3}$, and the slope $m =-\frac{2}{3}$.

Step3: Find the slope of each option

For the line $2x-3y = 10$, rewrite it as $-3y=-2x + 10$ or $y=\frac{2}{3}x-\frac{10}{3}$, slope is $\frac{2}{3}$.
For the line $3x + 2y=10$, rewrite it as $2y=-3x + 10$ or $y=-\frac{3}{2}x + 5$, slope is $-\frac{3}{2}$.
For the line $2x+3y = 10$, rewrite it as $3y=-2x + 10$ or $y=-\frac{2}{3}x+\frac{10}{3}$, slope is $-\frac{2}{3}$.
For the line $3x-2y = 10$, rewrite it as $-2y=-3x + 10$ or $y=\frac{3}{2}x-5$, slope is $\frac{3}{2}$.

Answer:

$2x + 3y = 10$