If `x_1,x_2,x_3` as well as `y_1, y_2, y_3` are in G.P. with same common ratio, then prove that the points `(x_1, y_1),(x_2,y_2),a n d(x_3, y_3)` are collinear.

Explanation

since points are collinear we have to prove that area is zero .
`x_(2)=x_(1) r,x_(3)=x_(1)r^(2) " and "y_(2) =y_(1)r,y_(3)=y_(1)r^(2)`
`Delta= |{:(x_(1),,y_(1),,1),(x_(2),,y_(2),,1),(x_(3),,y_(3),,1):}|`
`= |{:(x_(1),,y_(1),,1),(rx_(1),,ry_(1),,1),(r^(2)x_(1),,r^(2)y_(1),,1):}|`
` =x_(1)y_(1) |{:(1,,1,,1),(r,,r,,1),(r^(2),,r^(2),,1):}|`
`=0`
Hence the points are collinear