SOLUTION: let: L1: y=3 and L2: x=3 prove that:slop(L1) × slop(L2) = - 1

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Question 1139999: let: L1: y=3 and L2: x=3 prove that:slop(L1) × slop(L2) = - 1
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let:
L%5B1%5D:+y=3
L%5B2%5D: x=3
prove that:
slope%28L%5B1%5D%29+%2A+slope%28L%5B2%5D%29+=+-+1+


origin with these two points form right triangle which has legs a,+b parallel to axes, with say a horizontal and b vertical
basic idea: if a right triangle has legs a, b parallel to axes, with say b vertical, and you rotate that right triangle by 90 degrees counterclockwise, the new triangle will have vertical side a and horizontal side -b.
Slope of first triangle's hypotenuse is b%2Fa.
Slope of new triangle's hypotenuse is a%2F%28-b%29+=+-a%2Fb.
Those hypotenuses are perpendicular, because of the 90 degree rotation, and the product of their slopes is:

%28b%2Fa%29+%28-a%2Fb%29+=+-1 .....in your case a=3, b=3
%283%2F3%29+%28-3%2F3%29+=+-1
%281%29+%28-1%29+=+-1
-1+=+-1->proven


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution by tutor @MathLover1 did not address the conditions of the problem; and her answer is therefore very wrong.

The proposition is NOT true; the product of the slopes of L1 and L2 is NOT -1.

The slope of L1 is 0, and the slope of L2 is undefined. The product of "0" and "undefined" is not -1.

Two lines for which the product of the slopes is -1 are perpendicular.

However, the product of the slopes of two perpendicular lines is -1 ONLY IF THE TWO LINES ARE NOT ONE HORIZONTAL AND ONE VERTICAL.