SOLUTION: Given the points A(3,1), B(6,y) and C(12,-2), find the value(s) of y for which AB is perpendicular to BC

Algebra ->  Points-lines-and-rays -> SOLUTION: Given the points A(3,1), B(6,y) and C(12,-2), find the value(s) of y for which AB is perpendicular to BC      Log On


   

Question 810421: Given the points A(3,1), B(6,y) and C(12,-2), find the value(s) of y for which AB is perpendicular to BC
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Slope for line AB is %28y-1%29%2F%286-3%29=%28y-1%29%2F3.
The slope wanted for line BC is -3%2F%28y-1%29.

What we should know is that the product of two slopes must be -1.
%28%28y-1%29%2F3%29%28-3%2F%28y-1%29%29=-1 but this does not solve anything.
We still want an expression for slope of BC, which is %28-2-y%29%2F%2812-6%29=-%282%2By%29%2F6.

Now use this in the "-1" equation.
%28%28y-1%29%2F3%29%2A%28-%282%2By%29%2F6%29=-1
%28%28y-1%29%2F3%29%28%282%2By%29%2F6%29=1
%28y-1%29%28y%2B2%29%2F%2818%29=1
%28y-1%29%28y%2B2%29=18
y%5E2%2By-2=18
y%5E2%2By-20=0 Fortunately, factorable.
(y+5)(y-4)=0

highlight%28y=-5%29 or highlight%28y=4%29