Question

please help asap!!! i dont understand it

Answer 1

Answer:

a

Step-by-step explanation:

A perpendicular bisector, intersects a line at its mid point and is perpendicular to it.

Calculate slope m using the slope formula

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

with (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13)

m = $\frac{13-1}{9-(-7)}$ = $\frac{12}{9+7}$ = $\frac{12}{16}$ = $\frac{3}{4}$

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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{3}{4} }$ = - $\frac{4}{3}$ ←  slope of perpendicular bisector

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

($\frac{x_{1}+x_{2} }{2}$, $\frac{y_{1}+y_{2} }{2}$ )

using (x₁, y₁ ) = (- 7, 1) and (x₂, y₂ ) = (9, 13) , then

midpoint = ( $\frac{-7+9}{2}$, $\frac{1+13}{2}$ ) = ( $\frac{2}{2}$, $\frac{14}{2}$ ) = (1, 7 )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - $\frac{4}{3}$ , then

y = - $\frac{4}{3}$ x + c ← is the partial equation

To find c substitute the midpoint (1, 7) into the partial equation

7 = - $\frac{4}{3}$ + c ⇒ c = $\frac{21}{3}$ + $\frac{4}{3}$ = $\frac{25}{3}$

y = - $\frac{4}{3}$ x + $\frac{25}{3}$ ← equation of perpendicular bisector