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)

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.

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

(-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.

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.

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

(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

(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

Thank you!

To check if the given equations are actually perpendicular bisectors of the line segments joining the two given points, you can follow these steps:

1. Find the midpoint of the line segment using the coordinates of the two given points. The midpoint can be calculated by using the formula:
Midpoint (M) = ((x1 + x2) / 2, (y1 + y2) / 2)

2. Calculate the slope of the line segment joining the two given points, using the formula:
Slope (m) = (y2 - y1) / (x2 - x1)

3. Find the negative reciprocal of the slope calculated in step 2. The negative reciprocal can be obtained by flipping the fraction and changing its sign.

4. Write the equation of the perpendicular bisector using the negative reciprocal of the slope and the midpoint coordinates. The equation should be in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Let's follow these steps for each given equation:

1. For the equation y = -3x + 1:
- Midpoint (M) = ((-5 + 1) / 2, (6 + 8) / 2) = (-2, 7)
- Slope (m) = (8 - 6) / (1 - (-5)) = 2 / 6 = 1/3
- Negative reciprocal of slope = -1 / (1/3) = -3
- The equation of the perpendicular bisector passing through the midpoint (-2, 7) with a slope of -3 is:
y = -3x + b
Substitute the coordinates of the midpoint to solve for the y-intercept b:
7 = -3(-2) + b
7 = 6 + b
b = 1
- Therefore, the equation of the perpendicular bisector should be y = -3x + 1, which matches the given equation.

2. For the equation y = (1/2)x - (3/4):
- Midpoint (M) = ((1 + 6) / 2, (4 + (-6)) / 2) = (3.5, -1)
- Slope (m) = (-6 - 4) / (6 - 1) = -10 / 5 = -2
- Negative reciprocal of slope = -1 / (-2) = 1/2
- The equation of the perpendicular bisector passing through the midpoint (3.5, -1) with a slope of 1/2 is:
y = (1/2)x + b
Substitute the coordinates of the midpoint to solve for the y-intercept b:
-1 = (1/2)(3.5) + b
-1 = 1.75 + b
b = -2.75
- Therefore, the equation of the perpendicular bisector should be y = (1/2)x - 2.75, which does not match the given equation.

3. For the equation y = (5/3)x - (17/3):
- Midpoint (M) = ((5 + 10) / 2, (10 + 7) / 2) = (7.5, 8.5)
- Slope (m) = (7 - 10) / (10 - 5) = -3 / 5
- Negative reciprocal of slope = -1 / (-3/5) = 5/3
- The equation of the perpendicular bisector passing through the midpoint (7.5, 8.5) with a slope of 5/3 is:
y = (5/3)x + b
Substitute the coordinates of the midpoint to solve for the y-intercept b:
8.5 = (5/3)(7.5) + b
8.5 = 12.5 + b
b = -4
- Therefore, the equation of the perpendicular bisector should be y = (5/3)x - 4, which does not match the given equation.

In conclusion, the first equation matches the equation for the perpendicular bisector, while the second and third equations do not.