A figure is transformed in the plane such that no point maps to itself. What type of transformation must this be?? a) dilation b) reflection c)rotation d) translation and why?

Question

A figure is transformed in the plane such that no point maps to itself. What type of transformation must this be?? a) dilation  b) reflection  c)rotation  d) translation   and why?

ranga · Answer

"no point maps to itself"
I think it is translation.  

A dilation in x or y causes x and y to be multiplied by a factor.  But if the point were the origin, then horizontal or vertical dilation will map origin onto itself.

Similarly, a reflection about the x-axis will map all points on the x-axis onto itself.  A reflection about the y-axis will map all points on the y-axis onto itself.  

A rotation about the the x-axis, y-axis or about the origin will map the origin onto itself.

But a translation will make all points move and therefore none of the point can map onto itself.