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Question 1154202: Pls help!!! I’m desperate!!!
The equation of the perpendicular bisector of the line segment joining the points $(-3,8)$ and $(-5,4)$ is $y = mx + b$. Find $m+b$.
Note: The perpendicular bisector of the line segment $\overline{AB}$ is the line that passes through the midpoint of $\overline{AB}$ and is perpendicular to $\overline{AB}$.
Thank you!!!
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!  .
D is the mid of BC
D(x1,y1)
x1= (-3-5)/2 =-4
y1= (8+4)/2 =6
slope of BC = (8-4)/(-3+5)= 2
Slope of AD = 1/2 ( it is perpendicular to BC)
Equation of AD = (y-y1)=m(x-x1)
(y-6)=1/2 * (x+4)
2y-12= x+4
2y = x+16
y= 1/2*x+8
compare with y= mx+b
m=1/2 and b =8
m+b = 1/2 +8
Answer by ikleyn(52799)  (Show Source):
You can put this solution on YOUR website! .
The solution by @mananth is INCORRECT, unfortunately.
So I came to provide a correct solution.
I copied and pasted the solution by @mananth, and then fixed/edited it, where required.
D is the mid of BC
D(x1,y1)
x1= (-3-5)/2 =-4
y1= (8+4)/2 =6
slope of BC = (8-4)/(-3+5)= 2
Slope of AD = -1/2 ( it is perpendicular to BC) <<<---=== it is first place, where I edit the solution by @mananth.
Surely, it implies changes in all lines that follow . . .
Equation of AD is (y-y1) = m(x-x1)
(y-6) = -1/2 * (x+4)
2y - 12 = -x - 4
2y = -x + 8
y= -1/2*x + 4
compare with y = mx + b
m = -1/2 and b = 4
m+b = -1/2 + 4 =   = 3.5. ANSWER
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If you really want to learn on how to solve such problems on your own, in this site there are lessons that cover this subject.
The lessons are
- Find the slope of a straight line in a coordinate plane passing through two given points
- Equation for a straight line having a given slope and passing through a given point
- Solving problems related to the slope of a straight line
- Equation for a straight line in a coordinate plane passing through two given points
- Equation for a straight line parallel to a given line and passing through a given point
- Equation for a straight line perpendicular to a given line and passing through a given point (*)
- Advanced problems on finding equations for straight lines
- OVERVIEW of lessons related to the slope of a straight line
The most relevant to your current problem is the lesson marked (*) in the list.
So start from this lesson.
But if you want to learn the subject in all its aspects, you need to read all these lessons.
Consider them as your textbook, handbook, tutorials and (free of charge) home teacher.
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