Suppose that the three points A, B and C in t | vedclass

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Question

(C) Let the coordinates be $A(x_1, y_1), B(x_2, y_2)$ and $C(x_3, y_3)$.According to the question,the $x$-coordinates and $y$-coordinates are in $GP$

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lie on a straight line

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(C) Let the coordinates be $A(x_1, y_1), B(x_2, y_2)$ and $C(x_3, y_3)$.According to the question,the $x$-coordinates and $y$-coordinates are in $GP$ with the same common ratio $r$.Let $x_1 = a, x_2 = ar, x_3 = ar^2$ and $y_1 = b, y_2 = br, y_3 = br^2$.Thus,the points are $A(a, b), B(ar, br)$ and $C(ar^2, br^2)$.The slope of $AB = \frac{br - b}{ar - a} = \frac{b(r - 1)}{a(r - 1)} = \frac{b}{a}$.The slope of $BC = \frac{br^2 - br}{ar^2 - ar} = \frac{br(r - 1)}{ar(r - 1)} = \frac{b}{a}$.Since the slope of $AB$ is equal to the slope of $BC$,the points $A, B$ and $C$ are collinear.Therefore,the points $A, B$ and $C$ lie on a straight line.

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 $C$

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