Visual Notes: Transformations of Figures
Key vocabulary (dashed blue = before, the pre-image; orange = after, the image)
Translation
A slide. Every square moves the same number of units the same way. Here: 3 units right.
Rotation
A turn around a fixed point (red). Here: 90° clockwise, one quarter-turn.
Reflection
A flip across a line. Each square lands the same distance from the line, on the other side.
Sequence
Two or more in a stated order. Here: reflect across the line, then translate 1 unit right.
Turning on tracing paper
Trace the figure, put your pencil on the red point, and turn the paper. Every quarter-turn is 90°. Clockwise goes the way a clock’s hands move (an arrow pointing up turns to point right); counterclockwise goes the other way.
Worked examples
180° ÷ 90° = 2 quarter-turns to the left. The arrow on the paper goes up → left → down.
The square 1 unit above the line lands 1 unit below it; the one 3 above lands 3 below. Top and bottom swap.
Order matters: slide first, then turn the slid figure around the red point.
Remember
- Compare with the pre-image: pick one square and follow it to its new place.
- Turns are checked for direction as well as amount: 180° clockwise and 180° counterclockwise land in the same place but turn opposite ways.
- A vertical line goes up and down; a horizontal line goes side to side.
- Translations, rotations and reflections keep lengths and angles the same: the image is congruent.