Question

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

Answer 1

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=-
`2`x+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=-
`2`x-
`2`

Hope this helps!! :D