Model with Mathematics Refer to the graphic novel frame below. The last step is shown on grid 6. The girls make a clockwise rotation of 90° and begin the dance again. On a separate sheet of paper, expand the grid and mark the ending spot of the second series.

Persevere with Problems Triangle ABC has vertices A(0, 4), B(0, -2), and C(2, 0). The triangle is reflected over the x-axis. Then the image is rotated 180° counterclockwise about the origin. What are the coordinates of the final image?

Persevere with Problems Triangle QRS is translated 7 units right, then rotated 90° clockwise about the origin. The vertices of triangle Q''R''S'' are Q''(6, -1), R''(0, -1), and S''(0, -7). Find the coordinates of ΔQRS.

Model with Mathematics A triangle is rotated 90° clockwise about the origin. Then the image is rotated 270° clockwise about the origin.

a. Complete the algebraic representation to explain the effect of the series of transformations performed.

(x, y) → (_____, _____) → (_____, _____)

b. Based on your answer to part a, what can you conclude about a rotation of 90° followed by a rotation of 270°.

Reason Inductively Will a geometric figure and its rotated image always, sometimes, or never have the same perimeter? Explain your reasoning.