2.02 Rotations

Pentagon ABCDE is shown on the coordinate plane below: If pentagon ABCDE is rotated 180° around the origin to create pentagon A′B′C′D′E′, what is the ordered pair of point A′?

(2, −4)

If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′ lie?

(−4, 1)

Triangles DEF and D′E′F′ are shown on the coordinate plane below: What rotation was applied to triangle DEF to create triangle D′E′F′?

90° clockwise

Which statement accurately describes how to perform a 90° counterclockwise rotation of point A (−1, −2) around the origin?

Create a circle with the origin as its center and a radius of the origin and point A, then locate a point on the circle that is 90° counterclockwise from point A.

Parallelogram JKLM is shown on the coordinate plane below: If parallelogram JKLM is rotated 270° clockwise around the origin, what are the coordinates of the endpoints of the side congruent to side JM in the image parallelogram?

J′(−2, −6); M′(1, −5)

Which statement accurately explains whether a reflection over the x-axis and a 180° rotation would map figure ACB onto itself?

No, A″C″B″ is located at A″(−1, 1), C″(−3, 4), and B″(−5, 1)

What set of reflections and rotations would carry rectangle ABCD onto itself?

Reflect over the y-axis, reflect over the x‒axis, rotate 180°

What set of transformations are applied to parallelogram ABCD to create A″B″C″D″?

Reflected over the x‒axis and reflected over the y-axis

What set of transformations could be applied to rectangle ABCD to create A″B″C″D″?

Reflected over the x‒axis and rotated 90° counterclockwise

What is the ordered pair of X′ after point X (3, 4) is rotated 180°?

X′ (−3, −4)