If A(x, y), B(1, 2) and C(2, 1) are the vertices of a triangle of area 6 square unit, show that x+y=15 or-9

The vertices of ΔABC are A(3, 0), B(0, 6) and (6, 9). A straight line DE divides AB and AC in the ratio 1:2 at D and E respectively, prove that

If (t, t - 2), (t + 3, t) and (t + 2, t + 2) are the vertices of a triangle, show that its area is independent of t.

Prove that the points (a, b+c), (b, c+a) and (c, a+b) are collinear.

If the points (x₁y₁), (x₂, y₂) and (x₃, y₃) be collinear, show that