Question

ABC~ DEF. What sequence of transformations will move ABC onto DEF?

A. A dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
B. A dilation by a scale factor of 1/2, centered at the origin, followed by the translation (x,y)-> (x+7,y)
C. The translation (x,y)->(x+7,y), followed by a dilation by a scale factor of 2 centered at the origin.
D. A dilation by a scale factor of 2, centered at the origin, followed by the translation (x,y)-> (x+7,y)

Answer 1

D. Dilation by 2, translation right by 7.

Explanation:

You want to know the sequence of transformations that maps ∆ABC to ∆DEF.

Scale factor

Segment DE is 8 units long, and located at x=7. Segment AB is 4 units long and located at x=0.

The scale factor is the ratio of segment lengths:

DE/AB = 8/4 = 2

Triangle DEF is dilated by a factor of 2 (eliminates B).

Translation

Triangle DEF is oriented the same way as triangle ABC, so there is no reflection involved (eliminates A). As we noted, segment DE is 7 units to the right of segment AB, so a translation of x ⇒ x+7 is involved.

Sequence

The translation must occur after the dilation about the origin (eliminates C). If it were to occur first, the translation would be multiplied by the scale factor, so that DE would end up at x=14.

The required sequence of transformations is ...

D. A dilation by a scale factor of 2, centered at the origin, followed by the translation (x, y) ⇒ (x+7, y).

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