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 [tex]m[/tex], then the slope of the line perpendicular to this line segment is [tex]\frac{-1}{m}[/tex].
The slope of the line segment can be found by the following:
[tex]\frac{8 - 4}{-8 - 4}[/tex]
[tex]\frac{4}{-12}[/tex]
[tex]\frac{-1}{3}[/tex]
This means that the slope of the perpendicular line is 3.
The equation of a line is [tex]y = mx + b[/tex], were [tex]m[/tex] is the slope and [tex]b[/tex] 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 [tex]b[/tex]:
[tex]6 = (3)(-2) + b[/tex]
[tex]6 = -6 + b[/tex]
[tex]b = 12[/tex]
Finally, the equation of the line is
[tex]y = 3x + 12[/tex]
