Q:

The equation of the perpendicular line

Accepted Solution

A:
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]