Question

Without using distance formula, show that the points A(12,8), B(-2,6) and C(6,0) form a right-angled triangle.

Answer 1

Slope of AB (m₁) = `(6 - 8)/(-2 - 12) = (-2)/(-14) = 1/7`

Slope of BC (m₂) = `(0 - 6)/(6 + 2) = (-3)/4`

Slope of AC (m₃) = `(0 - 8)/(6 - 12) = (-8)/(-6) = 4/3`

Slope of BC x Slope of AC = m₂ x m₃

                                          = `(-3)/4 xx 4/3`           

                                         = -1

`therefore` AC and BC are perpendicular to each other and ABC form a right angled traiangle.