Rotations

Figure 2 was constructed using figure 1.

For the transformation to be defined as a rotation, which statements must be true? Select three options.

• The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).

• The transformation is rigid.

• Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.

• Segment CP is parallel to segment CP'.

• If figure 1 is rotated 180° about point C, it will be mapped onto itself.

Tags

CCSS.HSG.CO.B.6

Triangle XYZ is rotated to create the image triangle X'Y'Z'.

Which rules could describe the rotation? Select two options.

• R0, 90°

• R0, 180°

• R0, 270°

• (x, y) → (–y, x)

• (x, y) → (–x, –y)

Tags

CCSS.HSG.CO.B.6

One vertex of a polygon is located at (3, –2). After a rotation, the vertex is located at (2, 3).

Which transformations could have taken place? Select two options.

• R0, 90°

• R0, 180°

• R0, 270°

• R0, –90°

• R0, –270°

Tags

CCSS.8.G.A.3

One vertex of a triangle is located at (0, 5) on a coordinate grid. After a transformation, the vertex is located at (5, 0).

Which transformations could have taken place? Select two options

• R0, 90°

• R0, 180°

• R0, 270°

• R0, –90°

• R0, –180°

Tags

CCSS.8.G.A.3

Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.

R (1, 1) R' (–1, –1)

S (3, 1) S' (–3, –1)

T (1, 6) T' (–1, –6)

Which best describes the transformation?

• The transformation was a 90° rotation about the origin.

• The transformation was a 180° rotation about the origin.

• The transformation was a 270° rotation about the origin.

• The transformation was a 360° rotation about the origin.

Tags

CCSS.HSG.CO.B.6

Triangle ABC was transformed using the rule (x, y) → (–y, x). The vertices of the triangles are shown.

A (–1, 1) A' (–1, –1)

B (1, 1) B' (–1, 1)

C (1, 4) C' (–4, 1)

Which best describes the transformation?

• The transformation was a 90° rotation about the origin.

• The transformation was a 180° rotation about the origin.

• Th The transformation was a 360° rotation about the origin. e transformation was a 270° rotation about the origin.

• The transformation was a 360° rotation about the origin.

Tags

CCSS.HSG.CO.B.6

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices

X'(–3, 1), Y'(0, 0), and Z'(–2, –1). Which rule describes the transformation?

• R0, 90°

• R0, 180°

• R0, 270°

• R0, 360°

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Parallelogram ABCD is rotated to create image A'B'C'D'

Which rule describes the transformation?

• (x, y) → (y, –x)

• (x, y) → (–y, x)

• (x, y) → (–x, –y)

• (x, y) → (x, –y)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

Quadrilateral ABCD is transformed according to the rule (x, y) → (y, –x). Which is another way to state the transformation?

• R0, 90°

• R0, 180°

• R0, 270°

• R0, 360°

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

A pentagon is transformed according to the rule R0, 180°. Which is another way to state the transformation?

• (x, y) → (–x, –y)

• (x, y) → (–y –x)

• (x, y) → (x, –y)

• (x, y) → (–x, y)

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5