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- 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

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- anonymous

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- 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

dont i have to find the slope between the points

- anonymous

The distance formula \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \)

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- anonymous

so i plug in 3,4 and 5,5

- anonymous

No, you do not need to find the slope because Pythagorean Theorem will tell you if it is right or not

- 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

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

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

You do not need to find the slope between the points.

- anonymous

i know its not a right triangle but the problem you did above isnt making sense to me.

- anonymous

nixy still there

- 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

thank you nixy.

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