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
Geometry
chestercat
  • chestercat
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anonymous
  • anonymous
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.
anonymous
  • anonymous
dont i have to find the slope between the points
anonymous
  • anonymous
The distance formula \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \)

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anonymous
  • anonymous
so i plug in 3,4 and 5,5
anonymous
  • anonymous
No, you do not need to find the slope because Pythagorean Theorem will tell you if it is right or not
anonymous
  • anonymous
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
anonymous
  • anonymous
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.
anonymous
  • anonymous
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
anonymous
  • anonymous
You do not need to find the slope between the points.
anonymous
  • anonymous
i know its not a right triangle but the problem you did above isnt making sense to me.
anonymous
  • anonymous
nixy still there
anonymous
  • anonymous
\[ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \] \[d = \sqrt{(5-3)^2+(5-4)^2} \] 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.
anonymous
  • anonymous
thank you nixy.

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