Show that the triangle with vertices A(2, −4), B(8, −8), and C(−2, −10) is a right triangle by using the converse of the Pythagorean We must first find the length of all three sides of the triangle

Question

please help me i am in trouble and i need many questions tonight if anyone kindly can stay with until i finish the homework please

Answer 1

A(2,-4), B(8,-8), C(-2,-10)

AB = sqrt[(-8+4)^2 + (8-2)^2]

AB = sqrt[(-4)^2 + (6)^2]

AB = sqrt[16 + 36]

AB = sqrt(52)

BC = sqrt[(-10+8)^2 + (-2-8)^2]

BC = sqrt[(-2)^2 + (-10)^2]

BC = sqrt[4 + 100]

BC = sqrt(104)

AC = sqrt[(-10+4)^2 + (-2-2)^2

AC = sqrt[(-6)^2 + (-4)^2]

AC = sqrt[36 + 16]

AC = sqrt(52)

AB^2 + AC^2 = BC^2

sqrt(52)^2 + sqrt(52)^2 = sqrt(104)^2

52 + 52 = 104

Yes, it is a right triangle.