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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

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  1. jim_thompson5910
    • one year ago
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    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
    • one year ago
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    Sorry, I just saw this. I'll start on figuring that out right now. :)

  3. jim_thompson5910
    • one year ago
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    ok tell me what slopes you get

  4. anonymous
    • one year ago
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    http://sketchtoy.com/65524992

  5. jim_thompson5910
    • one year ago
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    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
    • one year ago
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    what did I do incorrectly with those?

  7. jim_thompson5910
    • one year ago
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    you have the correct slope for ST (middle calculation) so I'm going to do the other ones

  8. jim_thompson5910
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    Oh, I see now. Thanks! What do I do next?

  11. jim_thompson5910
    • one year ago
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    Summary of slopes slope of RS = 1/2 = 0.5 slope of ST = -4 slope of RT = -1

  12. jim_thompson5910
    • one year ago
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    do any of those slopes pair up and multiply to -1? if so, which two slopes do this?

  13. anonymous
    • one year ago
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    None of them.

  14. jim_thompson5910
    • one year ago
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    correct, so you don't have any perpendicular segments that means you don't have any right angles

  15. anonymous
    • one year ago
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    How do I show them how to make it a right angle?

  16. jim_thompson5910
    • one year ago
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    You would have to move one of the points to a place where you can get two slopes to multiply to -1

  17. anonymous
    • one year ago
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    Awesome. Thanks!

  18. jim_thompson5910
    • one year ago
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    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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