Question

A triangle has vertices A(2, 3), B(3,6), and C(6.5). Is this a right triangle? Justify with slope

Answer 1

No!

Because it doesn’t justify Pythagorean theorem.

D1= sqrtof( (3-2)^2+ (6-3)^2) = sqrtof 13

D2= sqrtof((6-3)^2+(5-6)^2)= sqrtof 10

D3= sqrtof((6-2)^2+(5-3)^2= sqrtof 20

Since D3 is longest, hypotenuse h= D3

Let’s p= D1 and b= D2

Pythagorean theorem is

p^2+b^2=h^2

If you place the value for p,b,h it doesn’t satisfy Pythagorean theorem. Thus, it is not right angle triangle.