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

Question

jim_thompson5910 · Answer

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.

anonymous · Answer

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

jim_thompson5910 · Answer

ok tell me what slopes you get

anonymous · Answer

http://sketchtoy.com/65524992

jim_thompson5910 · Answer

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.

anonymous · Answer

what did I do incorrectly with those?

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

None of them.

jim_thompson5910 · Answer

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

anonymous · Answer

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

jim_thompson5910 · Answer

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

anonymous · Answer

Awesome. Thanks!

jim_thompson5910 · Answer

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)