High School Geometry Rotation Test Questions with Solutions

📚 Quick Study Guide

• 📐 Definition of Rotation: A rotation is a transformation that turns a figure about a fixed point called the center of rotation.
• 🧭 Angle of Rotation: The amount of rotation, measured in degrees. A positive angle indicates a counterclockwise rotation, while a negative angle indicates a clockwise rotation.
• 📍 Center of Rotation: The fixed point around which the figure is rotated.
• 🔄 Rotational Symmetry: A figure has rotational symmetry if it can be rotated less than 360 degrees about a point so that the image coincides with the preimage.
• 🧭 Common Rotations in Coordinate Plane:
  • 90° counterclockwise rotation about the origin: $(x, y) \rightarrow (-y, x)$
  • 180° rotation about the origin: $(x, y) \rightarrow (-x, -y)$
  • 270° counterclockwise rotation about the origin: $(x, y) \rightarrow (y, -x)$
• 📝 Important Note: Rotations preserve the size and shape of the figure (i.e., they are rigid transformations).

Practice Quiz

1. What is the image of point $A(3, 4)$ after a $90^{\circ}$ counterclockwise rotation about the origin?
   1. (-4, 3)
   2. (4, -3)
   3. (-3, -4)
   4. (3, -4)
2. What is the image of point $B(-2, 1)$ after a $180^{\circ}$ rotation about the origin?
   1. (2, -1)
   2. (-2, -1)
   3. (2, 1)
   4. (-1, 2)
3. What is the image of point $C(5, -3)$ after a $270^{\circ}$ counterclockwise rotation about the origin?
   1. (-3, -5)
   2. (3, 5)
   3. (-5, 3)
   4. (3, -5)
4. A triangle has vertices $D(1, 1)$, $E(4, 1)$, and $F(1, 5)$. What are the coordinates of the vertices after a $90^{\circ}$ clockwise rotation about the origin?
   1. D'(-1, 1), E'(-1, 4), F'(-5, 1)
   2. D'(1, -1), E'(1, -4), F'(5, -1)
   3. D'(-1, -1), E'(-4, -1), F'(-1, -5)
   4. D'(1, 1), E'(4, 1), F'(1, 5)
5. A square has vertices $G(2, 2)$, $H(5, 2)$, $I(5, 5)$, and $J(2, 5)$. What are the coordinates of the vertices after a $180^{\circ}$ rotation about the origin?
   1. G'(-2, -2), H'(-5, -2), I'(-5, -5), J'(-2, -5)
   2. G'(2, -2), H'(5, -2), I'(5, -5), J'(2, -5)
   3. G'(-2, 2), H'(-5, 2), I'(-5, 5), J'(-2, 5)
   4. G'(2, 2), H'(5, 2), I'(5, 5), J'(2, 5)
6. What single transformation is equivalent to a $90^{\circ}$ counterclockwise rotation followed by another $90^{\circ}$ counterclockwise rotation?
   1. $90^{\circ}$ clockwise rotation
   2. $180^{\circ}$ rotation
   3. $270^{\circ}$ counterclockwise rotation
   4. $360^{\circ}$ rotation
7. Which point remains unchanged after a rotation of 360 degrees about the origin?
   1. (1, 0)
   2. (0, 1)
   3. (0, 0)
   4. (1, 1)