Question

The equation of the perpendicular line

Answer 1

Answer:

Step-by-step explanation:

First we need to find the point that the perpendicular line goes through on this line segment. The problem says it's a perpendicular bisector, which means it goes through the middle of the line, which means the point it goes through is halfway between (4, 4) and (-8, 8). This point would be (-2, 6).

Next, we need to find the slope of the perpendicular line. We know that if the slope of the line segment we're given is $m$, then the slope of the line perpendicular to this line segment is $\frac{-1}{m}$.

The slope of the line segment can be found by the following:

$\frac{8 - 4}{-8 - 4}$

$\frac{4}{-12}$

$\frac{-1}{3}$

This means that the slope of the perpendicular line is 3.

The equation of a line is $y = mx + b$, were $m$ is the slope and $b$ is the Y-intercept.

We know the slope, we so we just need to determine the Y-intercept. To do so, we can plug in a point that we know the line goes through, (-2, 6), and solve for $b$:

$6 = (3)(-2) + b$

$6 = -6 + b$

$b = 12$

Finally, the equation of the line is

$y = 3x + 12$