Question

Indicate the equation of the given line in standard form, writing the answer below.

Answer 1

Answer: $y-\frac{11}{2}=6(x-2)$

Step-by-step explanation:

For it to bisect the segment, we need to find the midpoint.

The midpoint is $\left(\frac{-1+5}{2}, \frac{6+5}{2} \right)=\left(2, \frac{11}{2} \right)$.

Now, for it to be perpendicular, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the given segment is $\frac{6-5}{-1-5}=-\frac{1}{6}$, so the slope of the perpendicular bisector is 6.

Thus, the equation of the line in point-slope form is $\boxed{y-\frac{11}{2}=6(x-2)}$