SOLUTION: State the value of "n" such that ∠XYZ is a right angle. X(2, 1) Y(n, n) Z(2 + n, 2) The answer is (3, 2), but not sure how to show the work.

Algebra ->  Angles -> SOLUTION: State the value of "n" such that ∠XYZ is a right angle. X(2, 1) Y(n, n) Z(2 + n, 2) The answer is (3, 2), but not sure how to show the work.       Log On


   



Question 1103236: State the value of "n" such that ∠XYZ is a right angle.
X(2, 1) Y(n, n) Z(2 + n, 2)
The answer is (3, 2), but not sure how to show the work.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The lines XY and XZ have to be perpendicular.
The slope of XY is (n-1)/(n-2)
The slope of YZ is (2-n)/(2)
Their product is -1, because the lines are perpendicular.
(n-1)/(n-2)*(2-n)/2=-1
(n-1)(2-n)=-1(2n-4)=-2n+4
2n-n^2-2+n=-2n+4
0=n^2-2n+4-3n+2=n^2-5n+6
0=(n-3)(n-2)
n=3, 2