For the triangle ABC formed by the points A (4, -6), B (3, -2) and C (5, 2), verify that median divides the triangle into two triangles of equal area.

⸪ AD is the median, D is the mid-point of B and C.

Co-ordinates of D = =

Area of triangle (x₁ (y₂ – y₃) + x₂ (y₃ – y₁) + x₃ (y₁ – y₂))

⸫ Area of ΔABD =

= = -3 sq. units

= 3 sq. units [⸪ Area cannot be negative]

⸫ Area of ΔADC =

= = -3 sq. units

= 3 sq. units [⸪ Area cannot be negative]

⸫ ar (ΔABD) = ar (ΔADC) = 3 sq. units

⸫ The median divides the triangle into two equal areas.