Write the algebraic representation of the dilation shown.

Critique Reasoning The set for a school play needs a replica of a historic building painted on a backdrop that is 20 feet long and 16 feet high. The actual building measures 400 feet long and 320 feet high. A stage crewmember writes (x, y) → (\(\large\frac{1}{12}x,\large\frac{1}{12}y\)) to represent the dilation. Is the crewmember’s calculation correct if the painted replica is to cover the entire backdrop? Explain.

Communicate Mathematical Ideas Explain what each of these algebraic transformations does to a figure.

a. (x, y) → (y, -x)

b. (x, y) → (-x, -y)

c. (x, y) → (x, 2y)

d. \((x, y) → (\cfrac{2}{3}x, y )\)

e. (x, y) → (0.5x, 1.5y)

Communicate Mathematical Ideas Triangle ABC has coordinates A(1, 5), B(-2, 1), and C(-2, 4). Sketch triangle ABC and A′B′C′ for the dilation (x, y) → (-2x, -2y). What is the effect of a negative scale factor?