Question

select the correct answer.
$overleftrightarrow{ab}$ and $overleftrightarrow{bc}$ form a right angle at point $b$. if $a = (-3, -1)$ and $b = (4, 4)$, what is the equation of $overleftrightarrow{bc}$?
a. $x + 3y = 16$
b. $2x + y = 12$
c. $-7x - 5y = -48$
d. $7x - 5y = 48$

Explanation:

Step1: Find slope of $\overrightarrow{AB}$

Slope formula: $m_{AB}=\frac{y_2-y_1}{x_2-x_1}$
$m_{AB}=\frac{4-(-1)}{4-(-3)}=\frac{5}{7}$

Step2: Find slope of $\overrightarrow{BC}$

Perpendicular slopes: $m_{BC}=-\frac{1}{m_{AB}}$
$m_{BC}=-\frac{7}{5}$

Step3: Write line equation for $\overrightarrow{BC}$

Point-slope form: $y-y_1=m(x-x_1)$
$y-4=-\frac{7}{5}(x-4)$

Step4: Simplify to standard form

Multiply by 5, rearrange terms:
$5(y-4)=-7(x-4)$
$5y-20=-7x+28$
$7x+5y=48$ or $-7x-5y=-48$

Answer:

C. $-7x - 5y = -48$