Compositions of Transformations

The coordinates of quadrilateral ABCD before and after a rotation about the origin are shown in the table. Find the angle of rotation.

The coordinates of triangle XYZ before and after a rotation about the origin are shown in the table. Find the angle of rotation.

The point (–2, 4) was rotated about the origin so that its new coordinates are (–4, –2). What was the angle of rotation?

Quadrilateral RSTU has vertices R(1, –1), S(4, –2), T(3, –4), and U(1, –3). Graph RSTU and its image after a translation along 〈–4, 1〉 and a reflection in the x-axis. Which point is located at (–3, 0)?

ΔJKL has vertices J(2, 3), K(5, 2), and L(3, 0). Graph ΔTUV and its image after a translation along 〈3, 1〉 and a rotation 180° about the origin. What are the new coordinates of L''?

Copy and reflect figure ABC in line s and then line t. Then describe a single transformation that maps ABC onto A''B''C''.

What transformation must occur to the brick at point M to further complete the pattern shown here?

What transformation must occur to the brick at point M to further complete the pattern shown here?