Question

3. Do these three points create a right triangle?
A(2,2) B(-2-1) C(-3, 2)

Answer 1

they do NOT create a right-angled triangle

Explanation:

to make a right-angled triangle the side lengths must comply with Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

the side lengths in this ABC triangle are :

AB² = (2 - -2)² + (2 - -1)² = 4² + 3² = 16 + 9 = 25

AB = 5

BC² = (-2 - -3)² + (-1 - 2)² = 1² + (-3)² = 1 + 9 = 10

BC = sqrt(10)

CA² = (-3 - 2)² + (2 - 2)² = (-5)² + 0² = 25

CA = 5

so, this is an isoceles triangle (2 equal legs).

the side lengths 5, 5, sqrt(10) do NOT create a right-angled triangle.

no matter how we combine their squares in the Pythagoras formula, it does not work :

10 = 25 + 25 = 50 no.

25 = 10 + 25 = 35 no.

Answer 2

Yes, they make a right triangle