Geometric Transformations

A triangle has vertices at A (1, 3), B (4, 2), and C (3, 8). Which transformation would produce an image with vertices A′(3, −1), B′(2, −4), C′(8, −3)?

• a reflection over the x-axis

• a reflection over the y-axis

• a rotation 90° clockwise

• a rotation 90° counterclockwise

A triangle has vertices at F (−7, 3), G (2, 6), and H (3, 5). What are the coordinates of each vertex if the triangle is reflected over the x axis?

• F′(−7, −3), G′(2, −6), H′(3, −5)

• F′(7, −3), G′(−2, −6), H′(−3, −5)

• F′(7, 3), G′(−2, 6), H′(−3, 5)

• F′(−7, 3), G′(−2, 6), H′(−3, −5)

Describe the transformation done on ΔRTS to form ΔVXW.

• rotation around the origin 180°

• reflection over the x-axis

• reflection over the y-axis

• translation

What are the coordinates of each vertex if the figure is rotated 90° counterclockwise about the origin?

• A'(−2, 2), B'(−5, −2), C'(−3, −6), D'(3, −4)

• A'(2, −2), B'(5, 2), C'(3, 6), D'(−3, 4)

• A'(−2, −2), B'(−5, 2), C'(−3, 6), D'(3, 4)

• A'(2, 2), B'(5, −2), C'(3, −6), D'(−3, −4)

Describe the transformation done on ΔFKW to form ΔRNG.

• rotation about the origin 90° counterclockwise

• rotation about the origin 90° clockwise

• reflection over the x-axis

• translation 5 units right and 9 units up

A triangle has vertices at A(−3, −1), B(−6, −5), C(−1, −4). Which transformation would produce an image with vertices A′(3, −1), B′(6, −5), C′(1, −4)?

• a. a reflection over the x-axis

• b. a reflection over the y-axis

• c. a rotation 90° clockwise

• d. a rotation 90° counterclockwise

A triangle has vertices at A(−7, 6), B(4, 9), C(−2, −3). What are the coordinates of each vertex if the triangle is translated 4 units right and 6 units down?

• A′(−11, 12), B′(0, 15), C′(−6, 3)

• A′(−11, 0), B′(0, 3), C′(−6, −9)

• A′(−3, 12), B′(8, 15), C′(2, 3)

• A′(−3, 0), B′(8, 3), C′(2, −9)

What are the coordinates of each vertex if the figure is rotated 180° clockwise about the origin?

• A′(−2, −2), B′(−5, 2), C′(−3, 6), D′(3, 4)

• A′(2, −2), B′(−2, −5), C′(−6, −3), D′(−4, 3)

• A′(−2, −2), B′(2, −5), C′(6, −3), D′(4, 3)

• A′(2, 2), B′(−2, 5), C′(−6, 3), D′(−4, −3)

In this figure, ΔXPL was formed by what transformation on ΔDWT?

• rotation about the origin 180°

• rotation about the origin 90° clockwise

• reflection over the x-axis

• rotation about the origin 90° counterclockwise

What are the coordinates of each vertex if the figure is reflected over the y-axis?

• A'(6, -1), B'(-5, 4), C'(-4, 5), D'(-3, 3)

• A'(-1, 6), B'(-4, 5), C'(-5, 4), D'(-3, 3)

• A'(-1, -6), B'(-5, -4), C'(-4, -5), D'(-3, -3)

• A'(-6, 1), B'(-5, 4), C'(-4, 5), D'(3, -3)