Question

10.4.2 quiz: transformations
abcd is rotated counterclockwise about the origin. by how many degrees
was abcd rotated?
a. 90°
b. 270°
c. 180°
d. 360°

Explanation:

Step1: Recall rotation rules

• Rotation of \(90^{\circ}\) counter - clockwise: \((x,y)\to(-y,x)\)
• Rotation of \(180^{\circ}\) counter - clockwise: \((x,y)\to(-x,-y)\)
• Rotation of \(270^{\circ}\) counter - clockwise: \((x,y)\to(y, - x)\)
• Rotation of \(360^{\circ}\) counter - clockwise: \((x,y)\to(x,y)\)

Step2: Check coordinates

Take a point, say \(A(3,3)\). After rotation, \(A'\) is \((- 3,-3)\) if rotated \(180^{\circ}\), but in the figure, if we consider the general position change.
Let's use the property of rotation. If we assume a point \((x,y)\) in the original figure \(ABCD\). For a \(270^{\circ}\) counter - clockwise rotation about the origin, the transformation rule is \((x,y)\to(y,-x)\).
If we consider the direction of rotation (counter - clockwise) and the position of the figure in the coordinate plane. A \(270^{\circ}\) counter - clockwise rotation moves the figure from the first - quadrant - like position (for \(ABCD\)) to the third - quadrant - like position (for \(A'B'C'D'\)) in the correct orientation.

Answer:

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