The points in the rectangular coordinate plane are transformed in such a way that each point A(x,y) is moved to a point `A'(kx,ky)`. If the distance between a point A and the origin is d, then the distance between the origin and thhe point A' is

Options

A. `k/d`
B. `d/k`
C. `d`
D. kd

Answer

D

Explanation

The distance between the origin and A is `d=sqrt(x^(2)+y^(2))`. The distance between the origin and `A'` is `sqrt((kx)^(2)+(ky)^(2))=sqrt(k^(2)(x^(2)+y^(2)))=ksqrt(x^(2)+y^(2))=kd`.