Question

If $x_1,x_2,x_3$ and $y_1,y_2,y_3$ are both in G.P with same common ratio then points $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$

• A. lie on a staright line
• B. are vertices of a triangle
• C. coincide with each other
• D. are vertices of an equilateral triangle

Answer 1

The correct option is A lie on a staright line

Let common ratio $=r$
$\Rightarrow x_2=x_1\cdot r,x_3=x_1\cdot r^2$ and
$\Rightarrow y_2=y_1\cdot r,y_3=y_1\cdot r^2$

Area of $△$ formed by them
$=\frac{1}{2}\left|\begin{array}{cccc}{x}_1& r{x}_1& r^2{x}_1& x_1\\ y_1& r{y}_1& r^2{y}_1& y_1\end{array}\right|=\frac{1}{2}|0+0+0|=0$ Sq. Units
So, points are collinear.