Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are (−3,4) and (−7,−6).

Answer 1

Answer:

She's right, praise jeebus :3

Step-by-step explanation:

Answer 2

Answer:

$y=-\frac{2}{5}x-3$

Step-by-step explanation:

First, you must find the midpoint of the segment, the formula for which is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$. This gives you (-5,-1) as the midpoint. This is the point at which the segment will be bisected.

Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula $\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$, which gives us a slope of $\frac{5}{2}$.

Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of $\frac{5}{2}$ is $-\frac{2}{5}$.

We now know that the perpendicular travels through the point (-5,-1) and has a slope of $-\frac{2}{5}$.

Solve for $b$ in $y=mx+b$.

$y=mx+b\\-1=-\frac{2}{5}(-5)+b\\-1=2+b\\-3=b\\b=-3$

Therefore, the equation of the perpendicular bisector is  $y=-\frac{2}{5}x-3$.