thenerdyjew

An iscoceles triangle is in the xy plane. The hypotenuse line segment has a slope of a, where a>2. What is the product of the three line segments' slopes?
1/a
-a
a
A^2
0

DrSteve

I assume you mean an isosceles right triangle since only right triangles have a hypotenuse. Then the two legs are perpendicular. This means that their slopes are negative reciprocals of each other. So the product of their slopes is -1. Therefore the product of the three slopes is (-1)a = -a.

Extra detail: If one of the legs has slope b, then the other leg has slope -1/b. So the product of the three slopes is b(-1/b)(a) = -a.

Technical note: This is not really a good problem. There is actually the possibility that the product is undefined. If the legs are parallel to the coordinate axes, then the vertical segment has an undefined slope. So clearly this is not an actual SAT question.

thenerdyjew

Yes, I meant an iscoceles right triangle. I think they avoided it by the >2 part. Thanks

DrSteve

You are right. I missed that. If the legs are parallel to the coordinate axes, then the slope of the hypotenuse will be 1 or -1.

Cokelly

Yeah, im pretty sure thats not a right triangle then. It would make it a lot easier to know one of yhe side lenghts but I aldo dont really understand your statements below.

Sent from my SGH-T959V using CC

emidank

nvm
10char

rspence

Problem's a little unclear...a could be infinitely large.

If a is a finite number, the other two legs are perpendicular, so the product of their slopes is -1. Therefore the product of all three slopes is -a.