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: Recall dilation and translation rules

A dilation of scale - factor $k$ through the origin maps a point $(x,y)$ to $(kx,ky)$. A translation of $a$ units to the right and $b$ units up maps a point $(x,y)$ to $(x + a,y + b)$.

Step2: Analyze the given transformation

The transformation maps a point $(x,y)$ to $(2x + 1,2y)$. First, if we consider the dilation part, a dilation of scale - factor 2 through the origin maps $(x,y)$ to $(2x,2y)$. Then, to get from $(2x,2y)$ to $(2x + 1,2y)$, we need to translate 1 unit to the right.

Answer:

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