Let a,b,c be in A.P and x,y,z be in G.P.. Then the points `(a,x),(b,y)` and `(c,z)` will be collinear if

Options

A. `x^2=y`
B. `x=y=z`
C. `y^2=z`
D. `x=z^2`

Answer

B

Explanation

Given that a,b,c are in A.P.
`rArra-b=b-c`
Now, `(a,x),(b,y)and (c,z)` are collinear.
`rArr(x-y)/(a-b)=(y-z)/(b-c)`
`rArr (x-y)/(y-z)=(a-b)/(b-c)=1`
`rArrx-y=y-z`
So, x,y,z are in A.P.
Thus x,y,z are in A.P and also in G.P.
`therefore x=y=z`.