Question

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.

Answer 1

First, we need to know how to transform a figure when we want to rotate it.

• If we rotate 90° clockwise, the transformation is from (x,y) to (y,-x), and counter clockwise is from (x,y) to (-y,x).
• If we rotate 180° in any direction, the transformation is from (x,y) to (-x.-y).
• If we rotate 270° clockwise, the transformation is from (x,y) to (-y,x). And counter clockwise is from (x,y) to (y,-x).

Now, we use these rules to match each statement with its right answer.

First statement:

The coordinates of D', if polygon ABCD rotates 90° counter clockwise to create A'B'C'D', would be (-2,2).

Second statement:

The coordinates of C'' , if polygon ABCD rotates 90° clockwise to create A''B''C''D'', would be (3,-1).

Third statement:

The coordinates of A''', if polygon ABCD rotates 180° clockwise to create polygon A'''B'''C'''D''', would be (4,-2).

Fourth statement:

The coordinates of B'', if polygon ABCD rotates 270° counterclockwise to create polygon A''B''C''D'', would be (4,2).

Answer 2

The answer is that if polygon ABCD rotates 90 counterclockwise to create a'b'c'd', then the coordinates of d will be at the location (-2, 2) and if the polygon ABCD rotates 180 clockwise to create a'b'c'd' the coordinate of A will become (3,-1).