Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Answer 1

Answer:

y = - $\frac{5}{2}$ x + $\frac{31}{2}$

Step-by-step explanation:

Calculate the slope m of BC using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = B (7, 5 ) and (x₂, y₂ ) = C (2, 3 )

$m_{BC}$ = $\frac{3-5}{2-7}$ = $\frac{-2}{-5}$ = $\frac{2}{5}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{2}{5} }$ = - $\frac{5}{2}$ , then

y = - $\frac{5}{2}$ x + c ← is the partial equation

To find c substitute A (3, 8 ) into the partial equation

8 = - $\frac{15}{2}$ + c ⇒ c = 8 + $\frac{15}{2}$ = $\frac{16}{2}$ +$\frac{15}{2}$ = $\frac{31}{2}$

y = - $\frac{5}{2}$ x + $\frac{31}{2}$ ← equation of perpendicular line