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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

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  1. anonymous
    • one year ago
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    Use the distance formula to find the sides of the triangle. After you have the sides by using the distance formula, you can use Pythagorean Theorem to tell if it is a right triangle.

  2. anonymous
    • one year ago
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    dont i have to find the slope between the points

  3. anonymous
    • one year ago
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    The distance formula \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \)

  4. anonymous
    • one year ago
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    so i plug in 3,4 and 5,5

  5. anonymous
    • one year ago
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    No, you do not need to find the slope because Pythagorean Theorem will tell you if it is right or not

  6. anonymous
    • one year ago
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    From R(3,4) to S(5,5) = \( d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \) \( d = \sqrt{(5-3)^2+(5-4)^2} \) = The side from R to S

  7. anonymous
    • one year ago
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    so the slope between r&s is (3,4)(5,5) which is 1/2 the we have to find the slope between s&t which is -4 then we have to find the slope between r & t which is -1 simplified.

  8. anonymous
    • one year ago
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    Once you have all your sides, \( a^2+b^2=c^ \) plugin for ab and c and they should equal each other if they don't then it is not a right triangle

  9. anonymous
    • one year ago
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    You do not need to find the slope between the points.

  10. anonymous
    • one year ago
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    i know its not a right triangle but the problem you did above isnt making sense to me.

  11. anonymous
    • one year ago
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    nixy still there

  12. anonymous
    • one year ago
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    \[ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \] \[d = \sqrt{(5-3)^2+(5-4)^2} \] R (3, 4), S (5, 5), and T (6, 1) From point R to S = a distance From point R to T = b distance From pont S to T = c distance ------------------------------------------------------ Lets find a, which is the distance between R and S \[ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \] \[d = \sqrt{(5-3)^2+(5-4)^2} =\sqrt{5} \] So a = \( \sqrt{5} \) ------------------------------------------------------- Now lets find b, which is the distance between R and T R (3, 4) and T (6, 1) \[d = \sqrt{(6-3)^2+(1-4)^2} =3\sqrt{2}\] --------------------------------------------------------- Now lets find c, which is the distance between S (5, 5), and T (6, 1) \[d = \sqrt{(6-5)^2+(1-5)^2} =\sqrt{17}\] -------------------------------------------------------- Now we have all our sides we can use \( a^2+b^=c^2 \) to tell if it is right and to prove our assumption \( \sqrt{5}^2+3\sqrt{2}^2 = \sqrt{17} ^2\) \( 23= 17\) <--- not true Since it is not true and 23 > 17 it is not a right triangle.

  13. anonymous
    • one year ago
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    thank you nixy.

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