Question

Prove that the triangle with vertices D(2,3), E(5,5), and F(4,0) is an isosceles triangle.

Answer 1

Answer: The bisector of angle F is a line segment from vertex F to the midpoint of line DE.

Midpoint: x = (2+6)/2 = 4; y = (-5+-1)/2 = -3

The midpoint is at (4,-3).

The equation of the line follows the point-slope formula:

y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁)

Substituting using points (5,6) and (4,-3)

y - 6 = [(⁻3 - 6)/(4 - 6)](x - 5)

y - 6 = (9/2)(x - 5)

2(y - 6) = 9(x - 5)

2y - 12 = 9x - 45

2y - 9x = -33