^_^0 Help with math please....

I'm extremely busy, and I can't remember how to do these three problems on my math hw.

Decide wheter the three points are vertices of a right triangle.
13. (3, 5) (-2, 4) (2, 10)
15. (-4, 1) (3, -2) (6, 5)
17. (1, 2) (-3, 6) (1, -5)

And not to mention I have a project due tomorrow, along with two major tests.

Kein Problem. I can help you with that. This may be complicated to explain but the simplest thing I can remember is graphing the three points and drawing the triangle. After that use the distance formula to find the lengths of all three sides. Then use Pythagorean's theorem to determine if it's a right triangle.

*Edit* I actually guess I made it harder than it had to be, just find the distance of all three lines using the distance formula and then use Pythagorean's theorem to see if it's a right triangle.

OK. I think I remember my teacher saying that...

I know there was an easier way with slope though. >.<

Slope is easy to find. Just rise over run. I use two of your vertices as an example:

Slope of (3,5) (-2,4): First subtract the first y coordinate from the second (5-5), so your y becomes -1.
Then do the same for the x, 3-(-2). So your x becomes five. So you put the y over the x and get 5 over -1. This gives you a slope of -5. Hope that helps you out.

Find the slope between the three points, meaning lines AB, AC, and BC. If none of these slopes are perpendicular, it cannot be a right triangle.

You could also plot the points on a graph, and look to see what kind of figure it creates.

If you plot it accurately on graph paper, or simply plot it well, you can see without doing all those equations.

^Yeah, but you can never assume, especially when you get into higher maths (and, we all know what "assuming" does...^_^). Although, of course, we all do it that way anyway, cuz it's a lot easier, and hey, what's a point or two if you're not correct??

But, go w/ what Scott said. It's the easiest way to find if it is a right triangle or not. And, you know if the two lines are perpendicular if their slopes are negative reciprocals of each other (like, -2 and 1/2).

Thankyou Scott. ^^ Big help. Again, thanks.