Two pages of visual notes for students to keep: the key words with grid pictures, every coordinate rule with an example, four solved problems in the style of the Let's Get to the Point game, and where transformations show up in real life. To make a PDF, click Print and choose "Save as PDF."
Visual Notes: Transformations
Grade 8 · CCSS 8.G.A.1 · Pairs with the Let's Get to the Point game
Name
The big idea: a transformation moves a shape. A translation slides it, a reflection flips it, and a rotation turns it. None of them change its size or shape, so the new shape is congruent to the old one. On a grid, each move has a rule for the coordinates.
Key vocabulary (red = before, the pre-image; blue = after, the image)
Transformation
A rule that moves or changes a figure on the grid.
Pre-image / image
The figure before (A) and after (A′, “A prime”) a move.
Translation
A slide: every point moves the same way. Here (x − 4, y − 3).
Reflection
A flip over a line. Over the y-axis: (x, y) → (−x, y).
Rotation
A turn around a point. 90° counterclockwise: (x, y) → (−y, x).
Rigid motion
A move that keeps size and shape: translations, reflections and rotations.
Congruent
Exactly the same size and shape, even if turned or flipped.
Every coordinate rule (each one moves P(3, 1) to P′)
Add 5 to each x: 5 right. Subtract 2 from each y: 2 down.
A(−4, 1) → A′(1, −1)
B(−2, 1) → B′(3, −1); C(−4, 4) → C′(1, 2)
✓ Check: every point moved the same way
2. Reflect over the x-axis
Flipping over the x-axis keeps x and changes the sign of y.
(1, 2) → (1, −2); (4, 2) → (4, −2)
(1, 4) → (1, −4)
✓ Check: each point is the same distance from the x-axis, on the other side
3. Rotate 90° counterclockwise
The rule: (x, y) → (−y, x). Swap, then make the new x its opposite.
(2, 1) → (−1, 2); (4, 1) → (−1, 4)
(4, 3) → (−3, 4)
✓ Check: the triangle turned a quarter turn, from quadrant I into quadrant II
4. Two moves in a row
Translate P(2, −3) by (x − 4, y + 1), then reflect over the x-axis.
Translate: (2 − 4, −3 + 1) = P′(−2, −2)
Reflect over the x-axis: P″(−2, 2)
✓ Check: do the moves in order; the second starts from P′
Watch out
Reflecting over the x-axis changes y (the point flips up or down), and over the y-axis changes x.
Counterclockwise is the opposite of the way clock hands move. 270° counterclockwise = 90° clockwise.
Label images with primes: A → A′ → A″.
Where you see it in real life
Elevators: a translation straight up or down.Butterflies: one wing is the reflection of the other.Ferris wheels: every car rotates around the center.Clocks: the hands turn clockwise.