Question

1. a polygon has been rotated about the origin. which statement must be true? a. the lengths of the sides are doubled. b. the area of the polygon did not change. c. the coordinates of the vertices did not change. d. the area of the polygon is 4 times its original area.

Explanation:

Rotation is a rigid transformation. Rigid transformations preserve the shape and size of the figure. So, the area of the polygon (which depends on its shape and size) remains the same.

• Option A: Rotation does not double the side - lengths. Only dilation (a non - rigid transformation in terms of size change) can change the side - lengths.
• Option C: When a polygon is rotated about the origin, the coordinates of its vertices change according to the rotation rules (e.g., for a rotation of \(90^{\circ}\) counter - clockwise about the origin, a point \((x,y)\) becomes \((-y,x)\)).
• Option D: As rotation is a rigid transformation, it does not multiply the area by 4.

Answer:

B. The area of the polygon did not change.