Question

answer this 42 question ​

Answer 1

To prove the points as collinear, we need to prove that the area of the triangle (made by these three points) is equal to zero.

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

=> Here, we have:

x1,y1 = a,b

x2,y2 = x,y

x3,y3 = a-x,b-y

Area of ∆ = 1/2(a(y-b+y)+x(b-y-b)+(a-x)(b-y))

=> 1/2(2ay-ab-xy+ab-ay-xb+xy)

=> 1/2(ay-bx)

Given that, ay = bx

=> 1/2(ay-ay) or 1/2(bx-bx)

=> 0

Since the area enclosed by the triangle formed by these three points is zero, they are collinear.

hence proved.