Question

write an equation of the perpendicular bisector of the line segment whose endpoints are (-1,1) and (7,-5)

Answer 1

can someone help me ?

Answer 2

Find the slope between those two points. The line perpendicular to that line will be the will have a slope that is the reciprocal of the slope between the original two points.

Answer 3

i tried it and was having difficulty

Answer 4

fist find the midpoint of the line
it is
\[(\frac{-1+7}{2},\frac{1-5}{2})=(3,-2)\]

Answer 5

okay that is what I got for the mid point

Answer 6

then find the slope of the line
it is \[\frac{1+5}{-1-7}=\frac{6}{-8}=-\frac{3}{4}\]

Answer 7

should be (2, -2) as midpoint. and the perpendicular slope is also the non negative reciprocal.

Answer 8

now you want the slope of the perpendicular line. it is the negative reciprocal of your slope, so change the sign and flip it

Answer 9

get \(\frac{4}{3}\)

Answer 10

y=(4/3)x-(8/3)

Answer 11

yes but it asks for perpendicular so that means you get the negative reciprocal which is \[4/3\]

Answer 12

now use the point slope formula
\[y-y_1=m(x-x_1)\] with \(m=\frac{4}{3}\) and either point you like

Answer 13

yes you are right, the slope is \(\frac{4}{3}\) for the perpendicular line

Answer 14

okay so now that we found the slope how do we find the equation

Answer 15

now we can write
\[y-1=\frac{4}{3}(x+1)\]and go from there

Answer 16

some algebra to finish up

Answer 17

okay let me do that

Answer 18

I got y = 4/3x - 5.9 is that right

Answer 19

how did I do with that. I dont think that this is correct

Answer 20

is anyone still there