SOLUTION: Line 1 is through (9,2) and (3,-8) and Line 2 is through (-3,5) and (5,-1) Are they perpendicular parallel or neither. Thanks in advance.

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Line 1 is through (9,2) and (3,-8) and Line 2 is through (-3,5) and (5,-1) Are they perpendicular parallel or neither. Thanks in advance.      Log On

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Question 91350: Line 1 is through (9,2) and (3,-8) and Line 2 is through (-3,5) and (5,-1)
Are they perpendicular parallel or neither. Thanks in advance.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope through (9,2) and (3,-8)
Solved by pluggable solver: Finding the slope
To find the slope going from (9,2) to (3,-8) we are going to calculate the change in y over the change in x, or the rise over the run. The change is the difference between the two coordinates. So if the y-coordinate of a point goes from 2 to -8, the change in these numbers is -10 (since -8-2=-10). If the x-coordinate changes from 9 to 3, then the change is -6 (since 3-9=-6). So to calculate the slope we use this formula:
Slope:

m=%28change_in_y%29%2F%28change_in_x%29=rise%2Frun where m is the slope

So now we let y%5B2%5D=-8,y%5B1%5D=2,x%5B2%5D=3,x%5B1%5D=9Now plug these numbers into the slope formula:

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=%28-8-%282%29%29%2F%283-%289%29%29+=+-10%2F-6


So after simplification the slope is m=5%2F3




Find the slope through (-3,5) and (5,-1)
Solved by pluggable solver: Finding the slope
To find the slope going from (-3,5) to (5,-1) we are going to calculate the change in y over the change in x, or the rise over the run. The change is the difference between the two coordinates. So if the y-coordinate of a point goes from 5 to -1, the change in these numbers is -6 (since -1-5=-6). If the x-coordinate changes from -3 to 5, then the change is 8 (since 5--3=8). So to calculate the slope we use this formula:
Slope:

m=%28change_in_y%29%2F%28change_in_x%29=rise%2Frun where m is the slope

So now we let y%5B2%5D=-1,y%5B1%5D=5,x%5B2%5D=5,x%5B1%5D=-3Now plug these numbers into the slope formula:

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29=%28-1-%285%29%29%2F%285-%28-3%29%29+=+-6%2F8


So after simplification the slope is m=-3%2F4



Since these two slopes are not equal, they are not parallel. Now multiply the two slopes

%285%2F3%29%28-3%2F4%29=-15%2F12=-5%2F4

Since this product doesn't equal -1, the two slopes are not perpendicular.