|
Question 252762: Here is my question:
My triangle points are A(2,5), B(12,-1) and C(-6,8).
What is the slope of the perpendicular bisector of AB? What is the slope of CL if CL is the altitude from point C?
I have been working on this for a while and appreciate any help with explanation.
Thanks.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! My triangle points are A(2,5), B(12,-1) and C(-6,8).
What is the slope of the perpendicular bisector of AB? What is the slope of CL if CL is the altitude from point C?
--------------------
Find the slope of AB.
m = diffy/diffx = (-1-5)/(12-2) = -6/10
m = -3/5 (slope of AB)
---------
The slope of lines perpendicular is the negative inverse, 5/3
-------------------------------------------------------------
For the midpoint of AB, get the average of x and y separately.
x: (2+12)/2 = 7
y: (5-1)/2 = 2
--> M(7,2) is the midpoint
-------------------------------
Now, find a line thru M with slope 5/3
Use y = mx + b to find b
2 = (5/3)*7 + b = 35/3 + b
b = -29/3
So the equation is:
y = (5/3)x - 29/3
-------------------
-------------------
What is the slope of CL if CL is the altitude from point C?
The altitude is also perpendicular, so its slope is 5/3, and it's thru the point C (-6,8).
-----------------------
Now, find a line thru C with slope 5/3
Use y = mx + b to find b
8 = (5/3)*(-6) + b = -10 + b
b = 18
So the equation is:
y = (5/3)x + 18
| |
|
| |
