Question

question 7 of 10
abcd is rotated counterclockwise about the origin. by how many degrees was abcd rotated?

Explanation:

Step1: Analyze the rotation of a single point

Take point \(A\). Assume the original coordinates of \(A\) are \((x,y)\). After rotation, observe its new position.

Step2: Use the rotation rules

For a counter - clockwise rotation about the origin:

• A \(90^{\circ}\) counter - clockwise rotation transforms \((x,y)\) to \((-y,x)\)
• A \(180^{\circ}\) counter - clockwise rotation transforms \((x,y)\) to \((-x,-y)\)
• A \(270^{\circ}\) counter - clockwise rotation transforms \((x,y)\) to \((y, - x)\)
• A \(360^{\circ}\) counter - clockwise rotation transforms \((x,y)\) to \((x,y)\)

Looking at the figure, if we consider the general position of the square \(ABCD\) and its image \(A'B'C'D'\), by comparing the orientation of the sides (e.g., the side \(AB\) in the original square and the corresponding side \(A'B'\) in the rotated square), we can see that it follows the \(270^{\circ}\) counter - clockwise rotation rule.

So, \(ABCD\) was rotated \(270^{\circ}\) counter - clockwise about the origin.

Answer:

C. \(270^{\circ}\)