Is by a(-4, 2), b(-2, 4), c(1, 3), d(2, 2).of ofto . of d′ if90° to a′b′c′d′ (-2, 2) of c″ if90° to a″b″c″d″ (4, -2) of a′′′ if° to a′′′b′′′c′′′d′′′ (3, -1) of b″ if° to a″b″c″d″ (4, 2)

D' = (-2 , 2)

C" = (3 , -1)

A''' = (4 , -2)

B" = (4 , 2)

Step-by-step explanation:

* Lets revise the rotation rules

- If point (x , y) rotated about the origin by angle 90° counterclockwise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 180° counterclockwise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° counterclockwise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180° clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° clock wise

∴ Its image is (-y , x)

- Lets solve the problem

∵ The polygon ABCD as a vertices:

   A = (-4 , 2) , B = (-2 , 4) , C = (1 , 3) , D = (2 , 2)

# Find the the coordinates of D′ if polygon ABCD rotates 90°

 counterclockwise to create A′B′C′D′

∵ D = (2 , 2)

∵ The image of the point (x , y) after rotating about the origin by angle

  90° counterclockwise is (-y , x)

∵ x = 2 , y = 2

∵ (-y , x) = (-2 , 2)

∴ D' = (-2 , 2)

# Find the coordinates of C″ if polygon ABCD rotates 90° clockwise

  to create A″B″C″D″

∵ C = (1 , 3)

∵ The image of the point (x , y) after rotating about the origin by angle

  90° clockwise is (y , -x)

∵ x = 1 , y = 3

∴ (y , -x) = (3 , -1)

∴ C" = (3 , -1)

# Find the coordinates of A′′′ if polygon ABCD rotates 180° clockwise

  to create A′′′B′′′C′′′D′′′

∵ A = (-4 , 2)

∵ The image of the point (x , y) after rotating about the origin by angle

  180° clockwise is (-x , -y)

∵ x = -4 , y = 2

∴ (-x , -y) = (4 , -2)

∴ A''' = (4 , -2)

# Find the coordinates of B″ if polygon ABCD rotates 270°

  counterclockwise to create A″B″C″D″

∵ B = (-2 , 4)

∵ The image of the point (x , y) after rotating about the origin by angle

  270° counterclockwise is (y , -x)

∵ x = -2 , y = 4

∴ (y , -x) = (4 , 2)

∴ B" = (4 , 2)

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