Question

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Answer 1

A sequence of transformations that maps △ABC to △A′B′C′ is a rotation of 90° counterclockwise about the origin followed by a translation 2 units right.

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection, or translation

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Answer 2

A sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.

What is the sequence of transformations?

The sequence of vertices ABC(DEF in this question) is clockwise, as is the sequence of A'B'C'(D'E'F in this question). Thus, an even number of reflections is involved, if any reflections are involved. The offered choices do not include suitable reflections.

The orientation of AB(DE) is toward the right. The orientation of A'B'(D'E') is up, so there must be a rotation of 90° CCW. Rotation of 90° CCW about the origin will leave the figure in a position that is 2 units left of where it is shown. The rotation must be followed by a translation 2 units to the right.

Thus, we conclude that a sequence of transformations that maps △DEF to △D′E′F′ is a rotation of 90° counterclockwise about the origin followed by a translation two units right.

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