Unit 9: Transformations — Homework 1: Translations

Graph and label each figure and its image under the given translation. Give the coordinates of the image for trapezoid STUV with vertices S(-3, 6), T(0, 7), U(1, 4), and V(-5, 2). Translation: (x, y) → (x + 7, y − 9). What are S′, T′, U′, and V′?

• S′(4, −3), T′(7, −2), U′(8, −5), V′(2, −7)

• S′(−10, 15), T′(−7, 16), U′(−6, 13), V′(−12, 11)

• S′(10, −12), T′(13, −11), U′(14, −14), V′(8, −16)

• S′(−3, −3), T′(0, −2), U′(1, −5), V′(−5, −7)

Graph and label each figure and its image under the given translation. Give the coordinates of the image for triangle ABC with vertices A(0, 7), B(7, 3), and C(1, 4). Translation: (x, y) → (x − 3, y − 4). What are A′, B′, and C′?

• A′(−3, 3), B′(4, −1), C′(−2, 0)

• A′(3, 11), B′(10, 7), C′(4, 8)

• A′(−3, 11), B′(4, 7), C′(−2, 8)

• A′(3, −11), B′(10, −7), C′(4, −8)

Graph and label each figure and its image under the given translation. Give the coordinates of the image for rhombus KLMN with vertices K(−3, 2), L(1, 4), M(−1, 0), and N(−5, −2). Translation: (x, y) → (x, y − 5). What are K′, L′, M′, and N′?

• K′(−3, −3), L′(1, −1), M′(−1, −5), N′(−5, −7)

• K′(2, −3), L′(6, −1), M′(4, −5), N′(0, −7)

• K′(−8, 7), L′(−4, 9), M′(−6, 5), N′(−10, 3)

• K′(−3, 7), L′(1, 9), M′(−1, 5), N′(−5, 3)

Graph and label each figure and its image under the given translation. Give the coordinates of the image for rectangle DEFG with vertices D(−4, 3), E(0, 2), F(−2, −6), and G(−6, −5). Translation: (x, y) → (x + 4, y + 1). What are D′, E′, F′, and G′?

• D′(0, 4), E′(4, 3), F′(2, −5), G′(−2, −4)

• D′(−8, 2), E′(−4, 1), F′(−6, −7), G′(−10, −6)

• D′(4, 1), E′(8, 0), F′(6, −8), G′(2, −7)

• D′(−4, 3), E′(0, 2), F′(−2, −6), G′(−6, −5)

Graph and label each figure and its image under the translation along the given vector. Identify the coordinates of the image for square PQRS with vertices P(−5, 4), Q(2, 8), R(6, 1), and S(−1, −3). Vector: ⟨2, −4⟩. What are P′, Q′, R′, and S′?

• P′(−3, 0), Q′(4, 4), R′(8, −3), S′(1, −7)

• P′(−7, 8), Q′(0, 12), R′(4, 5), S′(−3, 1)

• P′(−3, 8), Q′(4, 12), R′(8, 5), S′(1, 1)

• P′(−7, 0), Q′(0, 4), R′(4, −3), S′(−3, −7)

Graph and label each figure and its image under the translation along the given vector. Identify the coordinates of the image for triangle EFG with vertices E(−7, −7), F(−2, −3), and G(−1, −6). Vector: ⟨8, 3⟩. What are E′, F′, and G′?

• E′(1, −4), F′(6, 0), G′(7, −3)

• E′(−15, −10), F′(−10, −6), G′(−9, −9)

• E′(8, 3), F′(3, −1), G′(2, −3)

• E′(−1, −10), F′(4, −6), G′(5, −9)

Graph and label each figure and its image under the translation along the given vector. Identify the coordinates of the image for triangle JLM with vertices J(−5, 7), L(8, 3), and M(−3, −1). Vector: ⟨0, −5⟩. What are J′, L′, and M′?

• J′(−5, 2), L′(8, −2), M′(−3, −6)

• J′(−5, 12), L′(8, 8), M′(−3, 4)

• J′(−5, −2), L′(8, −7), M′(−3, −6)

• J′(0, 2), L′(13, −2), M′(2, −6)

Graph and label each figure and its image under the translation along the given vector. Identify the coordinates of the image for quadrilateral WXYZ with vertices W(1, 2), X(2, 7), Y(4, 5), and Z(6, 1). Vector: ⟨−7, −8⟩. What are W′, X′, Y′, and Z′?

• W′(−6, −6), X′(−5, −1), Y′(−3, −3), Z′(−1, −7)

• W′(8, 10), X′(9, 15), Y′(11, 13), Z′(13, 9)

• W′(−6, 6), X′(−5, 11), Y′(−3, 9), Z′(−1, 7)

• W′(1, 2), X′(2, 7), Y′(4, 5), Z′(6, 1)

K′(−8, 6) is the image of K after a translation along the rule (x, y) → (x − 3, y + 6). What are the coordinates of K?

• (−5, 0)

• (−11, 12)

• (−5, 12)

• (−8, 6)

P′(1, −2) is the image of P after a translation along the vector ⟨−8, 0⟩. What are the coordinates of P?

• (9, −2)

• (−7, −2)

• (1, −2)

• (9, 0)