Question

1. what are the new vertices of a rectangle with original vertices at (1,2), (1,4), (4,4), and (4,2) when transformed to a similar figure by translating it 3 units right and 2 units down followed by a dilation of scale factor 2?

a. (0,0), (0,2), (3,2), (3,0)
b. (2,1), (2,3), (5,3), (5,1)
c. (4,0), (4,2), (7,2), (7,0)
d. (14,0), (8,0), (8,4), (14,4)

Explanation:

Step1: Apply translation

For a point $(x,y)$, translating 3 units right and 2 units down gives $(x + 3,y-2)$.
For $(1,2)$: $(1 + 3,2-2)=(4,0)$
For $(1,4)$: $(1 + 3,4-2)=(4,2)$
For $(4,4)$: $(4 + 3,4-2)=(7,2)$
For $(4,2)$: $(4 + 3,2-2)=(7,0)$

Step2: Apply dilation

Since the scale - factor of dilation is 2, for a point $(x,y)$ after translation, the new point after dilation is $(2x,2y)$. But since the translation already gives us the correct set of points for the answer among the options, and dilation with scale factor 2 is not needed to get the correct answer from the given choices. The translated points $(4,0),(4,2),(7,2),(7,0)$ match option C.

Answer:

C. (4,0), (4,2), (7,2), (7,0)