AP EAMCET2016MathematicsStraight Lines
If x₁, x₂, x₃ as well as y₁, y₂, y₃ are in geometric progression with the same common ratio, then the points (x₁, y₁ ) , (x₂, y₂ ), (x₃, y₃ ) are
Options
- Avertices of an equilateral triangle
- Bvertices of a right angled triangle
- Cvertices of a right angled isosceles triangle
- Dcollinear
Correct answer
D. collinear
Step-by-step solution
It is given that x₁, x₂, x₃ and y₁, y₂, y₃ are in GP with the same common ratio. Let r be the common ratio. x₁=x₁, x₂=x r and x₃=x r^2 Similarly, y₁=y, y₂=y r and y₃=y r^2 Area of = 1 2 | array lll x₁ & y₁ & 1 x₂ & y₁ & 1 x₃ & y₁ & 1 array |= 1 2 | array ccc x & y₁ & 1 x r & y r & 1 x r^2 & y r^2 & 1 array |= 1 2 | array ccc 1 & 1 & 1 r & r & 1 r^2 & r^2 & 1 array |= 1 2 0=0 [ C ₁ . and C ₂ are identical] The given points do not form any triangle. They are collinear.