An equation for the perpendicular bisector of the line segment whose endpoints are (−4,−1) and (8,-5) is [tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]
Find the line [tex]$y=m x+b$[/tex] passing through [tex]$(-4,-1),(8,-5)$[/tex]
Compute the slope [tex]$(-4,-1),(8,-5): \quad m=-\frac{1}{3}$[/tex]
Compute the [tex]$y$[/tex] intercept: [tex]$\quad b=-\frac{7}{3}$[/tex]
Construct the line equation [tex]$y=m x+b$[/tex] where [tex]$m=-\frac{1}{3}$[/tex] and [tex]$b=-\frac{7}{3}$[/tex]
[tex]y=-\frac{1}{3} x-\frac{7}{3}[/tex]
A perpendicular bisector can be defined as a line that intersects another line segment perpendicularly and divides it into two parts of equal measurement. We can draw a perpendicular bisector using a rule, a compass and a pencil.
Two lines are said to be perpendicular to each other when they intersect each other at 90 degrees or at right angles. And, a bisector is a line that divides a line into two equal halves. Thus, a perpendicular bisector of a line segment AB implies that it intersects AB at 90 degrees and cuts it into two equal halves.
A line segment that bisects another line segment at a 90° angle is known as a perpendicular bisector. In other words, a perpendicular bisector divides a line segment into two equal parts by intersecting it at a 90° angle.
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