Rotations Assignment and Quiz

Which shows the image of quadrilateral ABCD after the transformation R0, 90°?

A

Which shows the image of rectangle ABCD after the rotation (x, y) → (-y, x)?

A

Which shows the image of triangle WXY after the transformation R0, -90°(x, y)?

C

Describe the general properties of rotations. Include a discussion of the properties of rigid transformations, and line segments connecting corresponding points to each other and to the center of rotation.

Rotations are rigid transformations, which means they preserve the size, length, shape, and angle measures of the figure. However, the orientation is not preserved. Line segments connecting the center of rotation to a point on the pre-image and the corresponding point on the image have equal length. The line segments connecting corresponding vertices are not parallel.

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.

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? Check all that apply.

R0, 270° R0, -90°

Examine the rotation. Which best describes point D?

center of rotation

Which shows the pre-image of quadrilateral W'X'Y'Z' before the figure was rotated according to the rule (x, y) → (-x, -y)?

C

A rectangle was rotated 270° about the origin. The image is shown. Which points are vertices of the pre-image? Check all that apply.

M(3, 2) N(3, 1)

After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6, 3), B'(-2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image? A - B - C -

A - (3,-6) B - (1,2) C - (7,-1)

Micaela tried to rotate the square 180° about the origin. Is her rotation correct? If not, explain why.

No, the vertices of the image and pre-image do not correspond.

After a rotation, A(-3, 4) maps to A'(4, 3), B(4, -5) maps to B'(-5, -4), and C(1, 6) maps to C'(6, -1). Which rule describes the rotation?

R0, 270°

A triangle has vertices at L(2, 2), M(4, 4), and N(1, 6). The triangle is transformed according to the rule R0, 180°. Which statements are true regarding the transformation? Check all that apply.

The rule for the transformation is (x, y) → (-x, -y). The coordinates of L' are (-2,-2). The coordinates of N' are (-1,-6).

A triangle has vertices at R(1, 1), S(-2, -4), and T(-3, -3). The triangle is transformed according to the rule R0, 270°. What are the coordinates of S'?

(-4, 2)

A triangle is rotated 90° about the origin. Which rule describes the transformation?

(x, y) → (-y, x)

Parallelogram ABCD is rotated to create image A'B'C'D'. Which rule describes the transformation?

(x, y) → (y, -x)

Triangle ABC was rotated about the origin. Which rule describes the rotation?

R0, 90°

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°

Which are not changed after a rotation? Check all that apply.

angle measures size shape position of center of rotation

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? Check all that apply.

R0, 90° R0, -270°