Question

Determine if the points of the vertices is a right triangle
(-3,2)
(-2,-4)
(3,3)

Answer 1

\[a ^{2}+b ^{2}=c ^{2}\]

Answer 2

You can only use pythagorean theorem if you know it's a right triangle, which you don't

Answer 3

I am having trouble applying the distance formula and setting it up for the pythagorean theorem.

Answer 4

Unfortunately you can't just find the distance and plug it in the pythagorean theorem because that is only used for when you know it's a right triangle

Answer 5

The distance between AB is Radical 37
The distance between AC is Radical 37
The distance between BC is Radical 74

Answer 6

I'm not sure how it is done but, teacher told me if the answer equals in the pythagorean theorem it's a right triangle

Answer 7

If that's the case, then you can just plug in the distances b/w AB, BC, CA in your a^2+b^2=c^2, choosing different lines (AB, BC, CA) as your hypotenuse and seeing if they equal

Answer 8

in terms of a^2+b^2=c^2, would it be AC^2+BC^2=AB^2

Answer 9

single opposite angle/vertices are the opposite sides

Answer 10

>>Unfortunately you can't just find the distance and plug it in the pythagorean theorem because that is only used for when you know it's a right triangle

Use the converse of the Pythagorean Theorem:

Get the lengths of the three sides and determine if the square of the longest side is equal to the sum of the squares of the other two sides.

Answer 11

Pythagorean Thereom converse:

If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/pythagconv.html

Answer 12

>>I'm not sure how it is done but, teacher told me if the answer equals in the pythagorean theorem it's a right triangle.

You are using Converse of Pythagorean Theorem to do this.

Answer 13

Assuming that these lengths are correct, here's what you do:

The distance between AB is Radical 37
The distance between AC is Radical 37
The distance between BC is Radical 74


If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

DOES (Radical 74)^2 = (Radical 37)^2 + (Radical 37)^2
DOES 74 = 37 + 37

YES, because 74 = 37 + 37 = 74

The triangle is a right triangle because it meets the requirements of the Converse of the Pythagorean Theorem. @DF001

Answer 14

Questions?