Question

AABC DEF. What sequence of transformations will move AABC onto ADEF?

A. A dilation by a scale factor of 2, centered at the origin, followed by
a 90° clockwise rotation about the origin

B. A dilation by a scale factor of, centered at the origin, followed by
the translation (x, y) - (x+4, y-2)

C. A dilation by a scale factor of, centered at the origin, followed by
a 180° clockwise rotation about the origin

D. A dilation by a scale factor of 2, centered at the origin, followed by
a reflection over the y-axis

Answer 1

C. Dilation by 1/2, rotation 180°

Explanation:

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

Points

We note that the coordinates of corresponding points are ...

• A = (-2, 2)
• D = (1, -1)

Comparing these, we find that D = (-1/2)·A.

The scale factor of -1/2 is equivalent to a dilation by a factor of 1/2 and reflection across the origin. Reflection across the origin is equivalent to a rotation of 180°.

Sequence

The sequence of transformations that moves ∆ABC to ∆DEF is ...

C. A dilation by a factor of 1/2 centered at the origin, followed by a 180° clockwise rotation about the origin.

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Additional comment

The direction of rotation is irrelevant when the rotation angle is 180°. When the center of dilation is unspecified, it is assumed to be the origin.

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