Question

Akhila says, "points A(1, 3), B(2, 2), C(5, 1) are collinear". Do you agree with Akhila? Why!?

Answer 1

The points will be collinear only if the triangle they form has an area of 0 sq units

Area of ∆ = 1/2(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))

When:

• (x1,y1) = (1,3)
• (x2,y2) = (2,2)
• (x3,y3) = (5,1)

=> Area of ∆ = 1/2(1(2-1) + 2(1-3) + 5(3-2))

=> Area of ∆ = 1/2(1 - 4 + 5)

=> Area of ∆ = 1

Since area of ∆ ≠ 0, the points aren't collinear.

Thus, I don't agree with Akhil