Suppose that the three points A, B and C in the plane are such that their x -coordinates as well as y -coordinates are in GP with the same common ratio. Then, the points A, B and C

Step-by-step solution

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=a r and x₃=a r^2 , y₁=b, y₂=b r and y₃=b r^2 Now, A(a, b), B(a r, b r), C (a r^2, b r^2 ) . Slope of A B= b( l -r) a( l -r) = b a and Slope of BC = b r(1-r) ar (1-r) = b a As slope of A B= Slope of B C A, B and C are collinear. A, B and C lie on a straight line.