Question

which transformation or set of transformations will map a point $(x,y)$ onto the point $(2x + 1,2y)$?
a a dilation of scale factor 2 through the origin followed by a translation of right 1 unit
b a dilation of scale factor 2 through the origin followed by a translation of up 1 unit
c a dilation of scale factor 2 through the point $(1,0)$
d a dilation of scale factor 2 through the point $(0,1)$

Explanation:

Step1: Analyze dilation through origin

A dilation of scale factor \(2\) through the origin maps \((x,y)\) to \((2x,2y)\).

Step2: Analyze translation

A translation of right \(1\) unit maps \((2x,2y)\) to \((2x + 1,2y)\).

Answer:

A. a dilation of scale factor 2 through the origin followed by a translation of right 1 unit