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?

Answer 1

Try drawing it out first

Answer 2

@ganeshie8

Answer 3

@whpalmer4

Answer 4

If (and only if) it is a right triangle, the lengths of the sides will satisfy the equation \[a^2+b^2=c^2\]where \(c\) is the length of the longest side. You can use the distance formula for the distance between two points \((x_1,y_1), (x_2,y_2)\) to find the lengths of the sides:
\[d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\]

Answer 5

do i plug the points into the formula?

Answer 6

Yes. For example, to find the distance between point R(3,4) = \((x_1,y_1)\) and T(6,1) = \((x_2,y_2)\):

\[d = \sqrt{(6-3)^2 + (1-4)^2} = \sqrt{3^2+(-3)^2} = \sqrt{9+9} = \sqrt{18} = 3\sqrt{2}\]

Answer 7

Find the length of the side between R and S, S and T, and R and T. Pick the largest one and let that be the value of \(c\). The other two will be \(a\) and \(b\). See if \[a^2+b^2=c^2\]If it does, you've got a right triangle. If not, you'll need to pick a set of points where that is true.

Answer 8

Than you

Answer 9

i got that it was a right triangle am i correct

Answer 10

No, I'm afraid not.

Distance between (3,4) and (6,1) is \(3\sqrt{2}\) as previously noted.

Distance between (3,4) and (5,5) is \[d = \sqrt{(5-3)^2+(5-4)^2} = \sqrt{5}\]Distance between (5,5) and (6,1) is\[d = \sqrt{(6-5)^2+(1-5)^2} = \sqrt{1+16} = \sqrt{17}\]There's no combination of the squares of those 3 that makes two of them add up to the other.

\[(\sqrt{5})^2 = 5\]\[(\sqrt{17})^2 = 17\]\[(3\sqrt{2})^2 = 18\]\[5+17\ne18\]

Answer 11

Just looking at this problem, how likely do you think it is that they'll ask you to do something for a second part of the problem, and then make the first part of the problem turn out to make the second part unnecessary? I'd say if you have a problem structured like this, and your answer for the first part turns out to be such that the second part doesn't have to be done, that's a clue to check your answer for the first part very carefully!