Question

Consider polygon PIKACU with endpoints P (2, -5), I (3, -2), K (4.5, -4), A (6, -2), C (7, -5), and U (4.5, -9). If PIKACU was rotated 90°, what is the sum of the x-coordinates of P'I'K'A'C'U'?

Answer 1

The sum of the x-coordinates of the vertices of polygon PIKACU after a 90° rotation is -27.

Step-by-step explanation:

To find the sum of the x-coordinates of the vertices of polygon PIKACU after a 90° rotation, we need to apply the rules of rotation about the origin. The rule for a 90° clockwise rotation (which is the same as -90° counterclockwise rotation) is (x, y) becomes (y, -x).

Applying this rule to each of the given coordinates, we get:
P' (-5, -2)
I' (-2, -3)
K' (-4, -4.5)
A' (-2, -6)
C' (-5, -7)
U' (-9, -4.5)

To find the sum of the x-coordinates, we simply add up the x values of these new points:
Sum of x-coordinates = (-5) + (-2) + (-4) + (-2) + (-5) + (-9)

The sum of the x-coordinates of P'I'K'A'C'U' is -27.