## anonymous one year ago Determine if triangle RST with coordinates R (3, 4), S (5, 5), and T (6, 1) is a right triangle. Use evidence to support your claim. If it is not a right triangle, what changes can be made to make it a right triangle? Be specific. @phi

1. jim_thompson5910

Find the slope of these segments: RS, ST, RT Use the slope formula $\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ If the product of any two slopes is -1, then those two segments are perpendicular, which leads to a right angle. If you have a right angle, you have a right triangle.

2. anonymous

Sorry, I just saw this. I'll start on figuring that out right now. :)

3. jim_thompson5910

ok tell me what slopes you get

4. anonymous
5. jim_thompson5910

You mixed up some of the numbers I think. The first calculation and third calculation is what I'm referring to. The second calculation is correct.

6. anonymous

what did I do incorrectly with those?

7. jim_thompson5910

you have the correct slope for ST (middle calculation) so I'm going to do the other ones

8. jim_thompson5910

R = (x1,y1) = (3,4) x1 = 3 y1 = 4 S = (x2,y2) = (5,5) x2 = 5 y2 = 5 ------------------------------------ slope of RS $\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $\Large m = \frac{5-4}{5-3}$ $\Large m = \frac{1}{2}$

9. jim_thompson5910

R = (x1,y1) = (3,4) x1 = 3 y1 = 4 T = (x2,y2) = (6,1) x2 = 6 y2 = 1 ------------------------------------ slope of RT $\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ $\Large m = \frac{1-4}{6-3}$ $\Large m = \frac{-3}{3}$ $\Large m = -1$

10. anonymous

Oh, I see now. Thanks! What do I do next?

11. jim_thompson5910

Summary of slopes slope of RS = 1/2 = 0.5 slope of ST = -4 slope of RT = -1

12. jim_thompson5910

do any of those slopes pair up and multiply to -1? if so, which two slopes do this?

13. anonymous

None of them.

14. jim_thompson5910

correct, so you don't have any perpendicular segments that means you don't have any right angles

15. anonymous

How do I show them how to make it a right angle?

16. jim_thompson5910

You would have to move one of the points to a place where you can get two slopes to multiply to -1

17. anonymous

Awesome. Thanks!

18. jim_thompson5910

For instance, moving point T from (6,1) to (7,1) will make slope of ST = -2 multiply the new slope of ST (-2) with the slope of RS (0.5) to get -2*0.5 = -1. So ST and RS are perpendicular. You have a right angle at point S. This is of course only after you move T to (7,1)