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10 votes
10 votes
Perpendicular bisector of the line segment whose endpoints are 7,4) and (−9,−4).

User MeghP
by
2.9k points

1 Answer

12 votes
12 votes

Answer:

y=-2x-2

Explanation:

If the endpoints of the line segment are (7,4) and (-9,-4), that means that the slope will be:


(-4-4)/(-9-7) =
(-8)/(-16)=
(1)/(2). For the perpendicular bisector to be perpendicular to the line, it must have a perpendicular slope, which will be the negative reciprocal of
(1)/(2), which is -
2. The perpendicular bisector must also go through the midpoint of the segment, which is (-1, 0) because -1 is the average of 7 and -9 and 0 is the average of 4 and -4.

Now we find the equation!

y=mx+b. Plug in -
2 as the "m", or slope:

y=-
2x+b

Now, plug in the point (-1, 0):

0=-
2*-1+b

0=
2+b

b=-
2

So, we have m=-
2 and b=-
2 and we can form our equation!

y=-
2x-
2

Hope this helps!! :D

User Jannis
by
2.9k points