Answer:
y=−1/5x+2
Step-by-step explanation:
First, you must find the midpoint of the segment, the formula for which is
(x1+x22,y1+y22)
. This gives (−5,3)
as the midpoint. This is the point at which the segment will be bisected.
Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula
y2−y1x2−x1
which gives us a slope of 5
Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of
5 is −1/5
We now know that the perpendicular travels through the point (−5,3)
and has a slope of −1/5
Solve for the unknown b in y=mx+b
3=−1/5(−5)+b⇒3=1+b⇒2=b
Therefore, the equation of the perpendicular bisector is
y=−1/5x+2
