anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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jim_thompson5910
  • 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.
anonymous
  • anonymous
Sorry, I just saw this. I'll start on figuring that out right now. :)
jim_thompson5910
  • jim_thompson5910
ok tell me what slopes you get

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anonymous
  • anonymous
http://sketchtoy.com/65524992
jim_thompson5910
  • 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.
anonymous
  • anonymous
what did I do incorrectly with those?
jim_thompson5910
  • jim_thompson5910
you have the correct slope for ST (middle calculation) so I'm going to do the other ones
jim_thompson5910
  • jim_thompson5910
R = (x1,y1) = (3,4) x1 = 3 y1 = 4 S = (x2,y2) = (5,5) x2 = 5 y2 = 5 ------------------------------------ slope of RS \[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\] \[\Large m = \frac{5-4}{5-3}\] \[\Large m = \frac{1}{2}\]
jim_thompson5910
  • jim_thompson5910
R = (x1,y1) = (3,4) x1 = 3 y1 = 4 T = (x2,y2) = (6,1) x2 = 6 y2 = 1 ------------------------------------ slope of RT \[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\] \[\Large m = \frac{1-4}{6-3}\] \[\Large m = \frac{-3}{3}\] \[\Large m = -1\]
anonymous
  • anonymous
Oh, I see now. Thanks! What do I do next?
jim_thompson5910
  • jim_thompson5910
Summary of slopes slope of RS = 1/2 = 0.5 slope of ST = -4 slope of RT = -1
jim_thompson5910
  • jim_thompson5910
do any of those slopes pair up and multiply to -1? if so, which two slopes do this?
anonymous
  • anonymous
None of them.
jim_thompson5910
  • jim_thompson5910
correct, so you don't have any perpendicular segments that means you don't have any right angles
anonymous
  • anonymous
How do I show them how to make it a right angle?
jim_thompson5910
  • jim_thompson5910
You would have to move one of the points to a place where you can get two slopes to multiply to -1
anonymous
  • anonymous
Awesome. Thanks!
jim_thompson5910
  • 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)

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