Alexandra drew the logo shown on half-inch graph paper. Write a rule that describes the translation Alexandra used to create the shadow on the letter A.

Kite KLMN has vertices at K(1, 3), L(2, 4), M(3, 3), and N(2, 0). After the kite is rotated, K′ has coordinates (-3, 1). Describe the rotation, and include a rule in your description. Then find the coordinates of L′, M′, and N′.

Make a Conjecture Graph the triangle with vertices (-3, 4), (3, 4), and (-5, -5). Use the transformation (y, x) to graph its image.

a. Which vertex of the image has the same coordinates as a vertex of the original figure? Explain why this is true.

b. What is the equation of a line through the origin and this point?

c. Describe the transformation of the triangle.

Critical Thinking Mitchell says the point (0, 0) does not change when reflected across the x- or y-axis or when rotated about the origin. Do you agree with Mitchell? Explain why or why not.

Analyze Relationships Triangle ABC with vertices A(-2, -2), B(-3, 1), and C(1, 1) is translated by (x, y) → (x - 1, y + 3). Then the image, triangle A′B′C′, is translated by (x, y) → (x + 4, y - 1), resulting in A″B″C″.

a. Find the coordinates for the vertices of triangle A″B″C″.

b. Write a rule for one translation that maps triangle ABC to triangle A″B″C″.