Question

1. here is triangle pog. match the description of the rotation with the image of pog under that rotation.

a. rotate 300 degrees clockwise around o.
b. rotate 60 degrees clockwise around o.
c. rotate 60 degrees clockwise around p.
d. rotate 240 degrees counterclockwise around o.
1.
2.
3.
4.
(from unit 1, lesson 13.)

Explanation:

Step 1: Understand rotation properties

A full - rotation is \(360^{\circ}\). Clockwise and counter - clockwise rotations are related. For example, a \(300^{\circ}\) clockwise rotation is equivalent to a \(60^{\circ}\) counter - clockwise rotation (\(360 - 300=60\)), and a \(240^{\circ}\) counter - clockwise rotation is equivalent to a \(120^{\circ}\) clockwise rotation (\(360 - 240 = 120\)).

Step 2: Analyze each option

• Option A: Rotate \(300^{\circ}\) clockwise around \(O\)

A \(300^{\circ}\) clockwise rotation around \(O\) is equivalent to a \(60^{\circ}\) counter - clockwise rotation around \(O\).

• Option B: Rotate \(60^{\circ}\) clockwise around \(O\)
• Option C: Rotate \(60^{\circ}\) clockwise around \(P\)
• Option D: Rotate \(240^{\circ}\) counter - clockwise around \(O\)

A \(240^{\circ}\) counter - clockwise rotation around \(O\) is equivalent to a \(120^{\circ}\) clockwise rotation around \(O\) (\(360-240 = 120\))

Step 3: Match the rotations

1. For the first image (not labeled with a number in the problem description but following the order of options), if we consider the orientation of the triangle with respect to the center of rotation:

• If we rotate \(\triangle POG\) \(60^{\circ}\) clockwise around \(P\) (Option C), we can get the corresponding image.

1. If we rotate \(\triangle POG\) \(240^{\circ}\) counter - clockwise around \(O\) (Option D), we can get the second image (in the order of the problem's non - numbered images). A \(240^{\circ}\) counter - clockwise rotation around \(O\) changes the position of the triangle such that the side lengths and angles are preserved, but the orientation with respect to \(O\) is as per the \(240^{\circ}\) counter - clockwise rule.
2. If we rotate \(\triangle POG\) \(60^{\circ}\) clockwise around \(O\) (Option B), we can get the third image. Using the rotation rules (the direction of rotation and the center \(O\)), we can map the vertices of \(\triangle POG\) to the vertices of the new triangle.
3. If we rotate \(\triangle POG\) \(300^{\circ}\) clockwise around \(O\) (Option A), since \(300^{\circ}\) clockwise is equivalent to \(60^{\circ}\) counter - clockwise around \(O\), we can get the fourth image.

Answer:

1. C. Rotate \(60\) degrees clockwise around \(P\)
2. D. Rotate \(240\) degrees counterclockwise around \(O\)
3. B. Rotate \(60\) degrees clockwise around \(O\)
4. A. Rotate \(300\) degrees clockwise around \(O\)