Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are (4,4) and (−8,8)

Answer 1

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