AP EAPCET 05-Jul-2022 Shift 1 Paper

Let the coordinate A(x1,y1),B(x2,y2) and C(x3,y3)
According to question, x-coordinate as well as y coordinates are in GP.
Let x1=a,x2=ar and x3=ar2, y1=b1y2=br and y3=br2
Now, A(a,b),B(ar,br),C(ar2,br2).
Slope of AB=‌

b(1−r)

a(1−r)

=‌

b

a

and
Slope of BC=‌

br(1−r)

ar(1−r)

=‌

b

a

As slope of AD− Slope of BC
∴A,B and C are collinear.
∴A,B and C lie on a straight line.