Examples of Rotations and Their Angles

📚 Quick Study Guide

• 📐 A rotation is a transformation that turns a figure around a fixed point called the center of rotation.
• 🧭 The angle of rotation specifies the number of degrees the figure is rotated.
• ➕ Rotations are positive (counterclockwise) by convention, unless stated otherwise.
• ➖ Negative rotations are clockwise.
• 🔄 A $90^{\circ}$ rotation turns a figure a quarter of a full circle.
• ↩️ A $180^{\circ}$ rotation turns a figure a half circle.
• ↪️ A $270^{\circ}$ rotation turns a figure three-quarters of a full circle.
• 📍 A $360^{\circ}$ rotation brings the figure back to its original position.

Practice Quiz

1. What is the image of point (1, 0) after a $90^{\circ}$ counterclockwise rotation about the origin?
   1. (0, 1)
   2. (0, -1)
   3. (1, 0)
   4. (-1, 0)


2. If a point is rotated $180^{\circ}$ about the origin, what changes occur to its coordinates?
   1. (x, y) becomes (-x, y)
   2. (x, y) becomes (x, -y)
   3. (x, y) becomes (-x, -y)
   4. (x, y) remains (x, y)


3. A square is rotated $90^{\circ}$ clockwise about its center. What does the square look like after the rotation?
   1. The square's orientation remains the same.
   2. The square is flipped horizontally.
   3. The square is flipped vertically.
   4. The square appears to have moved to a new location but is still a square.


4. What is the angle of rotation if a figure returns to its original position after four equal rotations?
   1. $45^{\circ}$
   2. $60^{\circ}$
   3. $90^{\circ}$
   4. $120^{\circ}$


5. Triangle ABC is rotated $270^{\circ}$ counterclockwise about the origin. If A is at (2,3), where will A' be located?
   1. (3, -2)
   2. (-3, 2)
   3. (-2, -3)
   4. (2, -3)


6. A regular pentagon is rotated about its center. What is the smallest angle of rotation that will map the pentagon onto itself?
   1. $36^{\circ}$
   2. $72^{\circ}$
   3. $90^{\circ}$
   4. $120^{\circ}$


7. What single rotation is equivalent to rotating a figure $180^{\circ}$ clockwise?
   1. $90^{\circ}$ counterclockwise
   2. $180^{\circ}$ counterclockwise
   3. $270^{\circ}$ counterclockwise
   4. $360^{\circ}$ counterclockwise