Question

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

Answer 1

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.

Answer 2

dont i have to find the slope between the points

Answer 3

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

Answer 4

so i plug in 3,4 and 5,5

Answer 5

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

Answer 6

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

Answer 7

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.

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

nixy still there

Answer 12

\[ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \]
\[d = \sqrt{(5-3)^2+(5-4)^2} \]

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
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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 = \( \sqrt{5} \)
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Now lets find b, which is the distance between R and T R (3, 4) and T (6, 1)
\[d = \sqrt{(6-3)^2+(1-4)^2} =3\sqrt{2}\]

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Now lets find c, which is the distance between S (5, 5), and T (6, 1)
\[d = \sqrt{(6-5)^2+(1-5)^2} =\sqrt{17}\]
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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.

Answer 13

thank you nixy.