Question

show that the triangle with vertices A(6,-7), B(11,-3), and C(2,-2) is a right triangle by using the converse of the Pythagorean Theorem. Find the area of the triangle

Answer 1

I can find the area of the triangle but idk how to do the converse part

Answer 2

ok but how do I find the converse of the Pythagorean theorem?

Answer 3

I updated the graphic with the lengths of each side

Answer 4

Hypotenuse² = 41 + 41
Hypotenuse² = 82
Hypotenuse = 9.0553851381

So, Pythagorean Theorem works out exactly.
I'd also say that since AC = AB, it is a 45 45 90 triangle

Answer 5

thanks

Answer 6

I might as well calculate the area too
Using Heron's formula for area when all 3 sides are known I get
area = 20.499999999789665
okay I guess that rounds to 20.5

Answer 7

Does that agree with your calculation for area?

Answer 8

i just left it as 20.48 but yeah

Answer 9

Heck, after all that work I'd say 20.48 is close to 20.5
all right !!!