Question

Polygons ABCD and A′B′C′D′ are shown on the following coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon ABCD is shown with vertex A on ordered pair 2, negative 2, vertex B on ordered pair 4, negative 2, vertex C on ordered pair 1, negative 3 and vertex D on ordered pair 5, negative 3. A polygon A prime B prime C prime D prime is shown with vertex A prime on ordered pair 1, 2 , vertex B prime on ordered pair 1, 4, vertex C prime on ordered 2, 1 and vertex D prime on ordered pair 2, 5. What set of transformations is performed on ABCD to form A′B′C′D′? (1 point) Select one: a. A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left b. A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin c. A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left d. A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin

Answer 1

The set of transformations that performed on ABCD to form A′B′C′D′ is "A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left" ⇒ a

Step-by-step explanation:

Let us revise some transformation

• If point (x , y) rotated about the origin by angle 90° counterclockwise, then its image is (-y , x)
• If point (x , y) rotated about the origin by angle 180° counterclockwise, then its image is (-x , -y)
• If point (x , y) rotated about the origin by angle 270° counterclockwise, then its image is (y , -x)
• If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)
• If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)

In polygon ABCD

∵ A = (2 , -2)

∵ B = (4 , -2)

∵ C = (1 , -3)

∵ D = (5 , -3)

In Polygon A'B'C'D'

∵ A' = (1 , 2)

∵ B' = (1 , 4)

∵ C' = (2 , 1)

∵ D' = (2 , 5)

By comparing the vertices and their images

∵ All x-coordinates of the vertices are the y-coordinates of

  their images

∵ All the signs of y-coordinates of the vertices are changed

- In rotation 90° counterclockwise we change the sign of

  the y-coordinate and switch the two coordinates

  (x , y) → (-y , x)

∴ A (2 , -2) → (2 , 2)

∴ B (4 , -2) → (2 , 4)

∴ C (1 , -3) → (3 , 1)

∴ D (5 , -3) → (3 , 5)

∴ Polygon ABCD is rotated 90° counterclockwise about the origin

∵ x-coordinate of each image is less then the x-coordinate

   of each vertex after the rotation by 1

- That means (x , y) → (x - 1 , y), then the polygon is translated

   1 unit to the left

∴ A' = (2 - 1 , 2) = (1 , 2)

∴ B' = (2 - 1 , 4) = (1 , 4)

∴ C' = (3 - 1 , 1) = (2 , 1)

∴ D' = (3 - 1 , 5) = (2 , 5)

∴ Polygon ABCD is translated 1 unit to the left after the rotation

The set of transformations that performed on ABCD to form A′B′C′D′ is "A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left"

Learn more:

You can learn more about transformation in brainly.com/question/9381523

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