Question

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

• A. lie on a straight line
• B. are vertices of an isosceles triangle
• C. are vertices of a scalene triangle
• D. are vertices of an equilateral triangle

Answer 1

The correct option is A lie on a straight line

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

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