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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