SOLUTION: Find the possible coordinates for A and B using the given slope of AB= -5/3 and Midpoint = (6,7)

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Question 987121: Find the possible coordinates for A and B using the given slope of AB= -5/3 and Midpoint = (6,7)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The midpoint is the average of x and y values of the endpoints.
x%5Bm%5D=%28x%5BA%5D%2Bx%5BB%5D%29%2F2=6
x%5BA%5D%2Bx%5BB%5D=12
x%5BA%5D=12-x%5BB%5D
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y%5Bm%5D=%28y%5BA%5D%2By%5BB%5D%29%2F2=7
y%5BA%5D%2By%5BB%5D=14
y%5BA%5D=14-y%5BB%5D
From the slope,
y%5BB%5D-y%5BA%5D=-%285%2F3%29%28x%5BB%5D-x%5BA%5D%29
3y%5BB%5D-3y%5BA%5D=-5x%5BB%5D%2B5x%5BA%5D
3y%5BB%5D-3%2814-y%5BB%5D%29=-5x%5BB%5D%2B5%2812-x%5BB%5D%29
3y%5BB%5D-42%2B3y%5BB%5D=-5x%5BB%5D%2B60-5x%5BB%5D
6y%5BB%5D-42=-10x%5BB%5D%2B60
6y%5BB%5D=-10x%5BB%5D%2B102
y%5BB%5D=-%285%2F3%29x%5BB%5D%2B17
So now you have a relationship between x%5BA%5D, y%5BA%5D, x%5BB%5D, and y%5BB%5D.
You're free to choose x%5BB%5D.
So when x%5BB%5D=0
y%5BB%5D=-%285%2F3%290%2B17=17
x%5BA%5D=12-0=12
y%5BA%5D=14-17=-3
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(0,17) and (12,-3) are one set of A-B points.