Question

Find an

Answer 1

Answer:

$y=-2x-4$

Step-by-step explanation:

Perpendicular Bisector

The bisector of a segment defined by points (x1,y1) and (x2,y2) must pass by the midpoint of the segment.

The midpoint (xm,ym) is calculated as follows:

$\displaystyle x_m=\frac{x_1+x_2}{2}$

$\displaystyle y_m=\frac{y_1+y_2}{2}$

The endpoints of the segment are (-3,-8) and (5,-4), thus the midpoint M is:

$\displaystyle x_m=\frac{-3+5}{2}=1$

$\displaystyle y_m=\frac{-8-4}{2}=-6$

Midpoint: M(1,-6)

Let's find the slope of the given segment. The slope can be calculated with the formula:

$\displaystyle m_1=\frac{y_2-y_1}{x_2-x_1}$

$\displaystyle m_1=\frac{-4+8}{5+3}=\frac{1}{2}$

If the bisector is also perpendicular, its slope m2 and the slope of the segment m1 must comply:

$m_1.m_2=-1$

Solving for m2:

$\displaystyle m_2=-\frac{1}{m_1}=-\frac{1}{\frac{1}{2}}=-2$

Once we have the slope -2 and the point through which our line must pass (1,-6), we compute the equation in its point-slope form:

$y-y_o=m(x-x_o)$

$y-(-6)=-2(x-1)$

Operating

$y+6=-2(x-1)$

$y+6=-2x+2$

Rearranging

$\boxed{y=-2x-4}$