Question

Prove that the points A(1,-1), B (2,-5) and C(-2,-4) are the vertices of an isosceles triangle. Given that M is the mid-point of the longest side of the triangle ABC, calculate the coordinates of M. ​

Answer 1

AB = √((2 - 1)² + (-5 - (-1))²) = √(1² + (-4)²)

= √(1 + 16) = √17

BC = √((2 - (-2))² + (-5 - (-4))²) = √(4² + (-1)²)

= √(16 + 1) = √17

AC = √((-2 - 1)² + (-4 - (-1))²) = √((-3)² + (-3)²)

= √(9 + 9) = √18 = 3√2

ABC is an isosceles triangle.

AC is the longest side.

M = ((1 + (-2))/2, (-1 + (-4))/2) = (-1/2, -5/2)

= (-.5, -2.5)