Question

Can someone please check my answers?
The question is: Write an equation for the perpendicular bisector of the line segment joining the two points.

(-5,6),(1,8)= y=-3x+1
(1,4),(6,-6)= y=(1/2)x-(3/4)
(5,10),(10,7)= y=(5/3)x-(17/3)

Answer 1

Plug in the (x,y) values and see whether they fit your equations.

-3(-5) + 1 = 6? No
(1/2)(1) - 3/4 = 4? No
(5/3)(5)-17/3 = 10? No

Try again, and show your work; you evidently need some coaching and study.

Answer 2

What am I doing wrong?

slope m=(8-6)/(1--5)= m=2/6= m=1/3 m=-3
midpoint (-5+1)/2, 8+6/2)= (-4/2, 14/2)= (-2, 7)
y=mx+b= 7=-3(-2)+b = 7=6+b = 1=b
equation y=-3x+1

Answer 3

(-5,6),(1,8)= y=-3x+1

m = (8-6)/1+5) = 2/6 = 1/3
so yes, your slope is -3
y = -3 x + b

now midpoint
x --> (-5 + 1)/2 = -2
y --> (6+8)/2 = 7
so yes the middle is at (-2 , 7)
7 = -3(-2) + b
7 = 6 + b
b = 1
so yes
y = -3 x + 1

THe original points are NOT on the bisector.

Answer 4

Perhaps I am not being clear. There is no reason the original pair of points would be on the perpendicular bisector of the line between them. In fact they better not be there.

Answer 5

Okay so I fixed the next two because I added the fractions wrong.
2. y=(1/2)x-(11/4)
3. y=(5/3)x-4

Answer 6

(1,4),(6,-6)= y=(1/2)x-(3/4)
m = (-6 -4)/(6-1) = -10/5 = -2
so your m = +1/2 check

x ---> (1+6)/2 = 7/2
y ---> (4-6)/2 = -1
so (7/2 , 1)
1 = (1/2)(7/2) + b
4/4 = 7/4 + b
b = -3/4
y = (1/2) x - 3/4
I like your first answer

Answer 7

(5,10),(10,7)= y=(5/3)x-(17/3)
m = (7-10)/(10-5) = -3/5
so your m = 5/3
y = (5/3) x + b

x --> 15/2
y --> 17/2
so through (15/2 , 17/2)

17/2 = (5/3)(15/2) + b
so
17/2 = 25/2 + b
b = - 8/2 = -4
y = (5/3) x - 4
agree with your second answer this time

Answer 8

Thank you!