Geometric Construction of a Rotation
Geometric Construction of a Rotation is a Grade 7 math skill in Reveal Math Accelerated, Unit 6: Congruence and Similarity, where students use a compass and protractor (or coordinate rules) to rotate a figure a specified number of degrees around a center of rotation, precisely locating the image of each vertex. Understanding rotations is fundamental to the study of rigid transformations and congruence.
Key Concepts
Property Before using algebra, we construct rotations physically using two tools: a protractor (to get the exact angle and direction) and a compass or ruler (to keep the distance from the center perfectly equal).
Examples Rotating Point P $70^\circ$ CCW around Center C: 1. Draw a straight guideline connecting center $C$ to point $P$. 2. Place the protractor on $C$, align it with the guideline, and mark a $70^\circ$ angle in the Counterclockwise direction. Draw a new ray through that mark. 3. Measure the exact distance from $C$ to $P$. Mark that same distance on the new ray. That spot is $P'$. Rotating a Triangle: To rotate triangle $DEF$, you must do the 3 step process above separately for corner $D$, then corner $E$, then corner $F$. Finally, connect the new dots to form $D'E'F'$.
Explanation Why do we do this? Doing it by hand proves why a rotation is a rigid motion. The protractor guarantees the angle is right, and the compass guarantees the shape doesn't stretch or shrink. When you do this on paper, physically turn the paper with your hands—it helps your brain visualize where the final image should land!
Common Questions
How do you construct a rotation of a figure?
For each vertex, measure the angle of rotation from the center of rotation using a protractor, and place the image vertex at the same distance from the center but at the rotated angle. Connect the image vertices to form the rotated figure.
What are the coordinate rules for common rotations?
For a rotation about the origin: 90 degrees counterclockwise maps (x, y) to (-y, x); 180 degrees maps (x, y) to (-x, -y); 270 degrees counterclockwise (or 90 clockwise) maps (x, y) to (y, -x).
What properties are preserved in a rotation?
Rotations are rigid transformations, so the shape, size, and side lengths of the figure are preserved. The image is congruent to the original figure.
What is Reveal Math Accelerated Unit 6 about?
Unit 6 covers Congruence and Similarity, including all four geometric transformations — translations, reflections, rotations, and dilations — and their relationships to congruence and similarity.