Question

triangle abc is similar to triangle def. write the equation, in slope - intercept form, of the side of triangle def that is parallel to bc. you must show all work to receive credit.

Explanation:

Step1: Find slope of BC

Assume B(5, 2), C(1, - 1). Slope $m_{BC}=\frac{2 - (-1)}{5 - 1}=\frac{3}{4}$.

Step2: Find a parallel - side in DEF

Assume D(3, - 4), E(5, - 2). Slope $m_{DE}=\frac{-2-(-4)}{5 - 3}=1$. Assume D(3, - 4), F(1, - 5). Slope $m_{DF}=\frac{-5-(-4)}{1 - 3}=\frac{1}{2}$. Assume E(5, - 2), F(1, - 5). Slope $m_{EF}=\frac{-5-(-2)}{1 - 5}=\frac{3}{4}$.

Step3: Use point - slope form to get equation

Using point E(5, - 2) and slope $m = \frac{3}{4}$, $y+2=\frac{3}{4}(x - 5)$.

Step4: Convert to slope - intercept form

$y+2=\frac{3}{4}x-\frac{15}{4}$, so $y=\frac{3}{4}x-\frac{15}{4}-2=\frac{3}{4}x-\frac{23}{4}$.

Answer:

$y=\frac{3}{4}x-\frac{23}{4}$