Question

b.e.s.t. test prep you use a coordinate plane to plan a shadow puppet show. what rotation about the origin can you use to represent the dog taking a drink of water?
a. clockwise 90°
b. counterclockwise 90°
c. 180°
d. 360°

Explanation:

Step1: Analyze rotation effects

A \(180^{\circ}\) rotation about the origin changes \((x,y)\) to \((-x,-y)\). A \(360^{\circ}\) rotation brings the figure back to its original position. A \(90^{\circ}\) clock - wise rotation changes \((x,y)\) to \((y,-x)\), and a \(90^{\circ}\) counter - clockwise rotation changes \((x,y)\) to \((-y,x)\).

Step2: Visualize the dog's position change

Assume the dog's initial position (before drinking water) and the position when drinking water. A \(180^{\circ}\) rotation would flip the dog completely. A \(360^{\circ}\) rotation is no change. For a \(90^{\circ}\) clock - wise rotation, if we consider the general orientation of the dog (say in the second quadrant initially), a \(90^{\circ}\) clock - wise rotation would re - orient it as if it is bending down (taking a drink). A \(90^{\circ}\) counter - clockwise rotation would orient it in the opposite non - drinking direction.

Answer:

A. Clockwise \(90^{\circ}\)