Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2). Match the coordinates of the points of the transformed polygons to their correct values. the coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ (-2, 2) the coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ (4, -2) the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ (3, -1) the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ (4, 2)

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is at (-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is at (3, -1)

The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is at (4, -2)

The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is at (4, 2)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its points are also transformed. Types of transformation are reflection, rotation, dilation and translation.

Given Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).

If a point X(x, y) is rotated 90° counterclockwise, the new location X' is at (-y, x)

If a point X(x, y) is rotated 90° clockwise, the new location X' is at (y, -x)

If a point X(x, y) is rotated 180° clockwise, the new location X' is at (-x, -y)

If a point X(x, y) is rotated 270° counterclockwise, the new location X' is at (y, -x)

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is at (-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is at (3, -1)

The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is at (4, -2)

The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is at (4, 2)