You have studied in Class IX, (Chapter 9, Example 3), that a median of a triangle divides it into two triangles of equal areas. Verify this result for engle ABC whose vertices are A(4, – 6), B(3, –2) and C(5, 2).

Coordinates pf mid-points of BC = D((x₁+y₂)/2, (y₁+y₂)/2) = D((3+5)/2, (-2+2)/2) = D(4, 0)
Area of triangle ABD
= 1/2[4(-2-0)+3{0-(-6)}+4{-6-(-2)}]
= 1/2[-8+18-16] = 1/2[-6] = -3 = 3 square units
Area of triangle ACD
= 1/2 [4(2-0)+5{0-(-6)}+4(-6-2)]
= 1/2 [8+30-32] = 1/2[6] = 3 square units
⇒ Area of triangle ABD = Area of trinagle ACD = 3 square units
Hence, a medium of a triangle divides it into two triangles of equal areas.

See the video explanation here✌️