Mrs.D Math · 8th Grade

TURNING
POINT

Properties of Rotations · Geometry
🔄 Rotation
🗘️ Turning
📌 Preimage → Image
↶ 90° Turn
↻ 180° Flip
🎯 About the Origin
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📚 Properties of Rotations

What Is a Rotation?

A rotation turns every point of a figure around a fixed center by a certain angle. In 8th grade we rotate about the origin (0, 0). The image stays congruent to the preimage — same size and shape, just turned.

↶
Direction matters! A turn can go counterclockwise (the positive direction) or clockwise. Always read both the degrees and the direction.
90° clockwise is NOT the same as 90° counterclockwise!
⟳
We use 90°, 180°, 270°, and 360°.
A 90° clockwise turn lands in the same spot as a 270° counterclockwise turn — and 180° and 360° look the same either way.

The Rotation Rules (about the origin)

These swap and change the signs of the coordinates.

↶
90° counterclockwise: (x, y) → (−y, x)
(3, 1) → (−1, 3)
↻
180°: (x, y) → (−x, −y)
(3, 1) → (−3, −1)
↷
270° counterclockwise: (x, y) → (y, −x)
(3, 1) → (1, −3)
⟳
360°: (x, y) → (x, y) — a full turn back to start.
↻
Going clockwise? Just swap: 90° clockwise uses the 270° rule (x, y) → (y, −x), and 270° clockwise uses the 90° rule (x, y) → (−y, x).
180° and 360° are the same in both directions.

How to Play

🔍
What Was the Rotation — Every question shows A and A′ on a graph. Easy: pick the turn in words (like “90° clockwise”). Medium: pick the rule with the words. Hard: pick the rule in (x, y) form.
📌
What Is the Image Point — Easy: tap the image point on the graph. Medium & Hard: a mix of graph tapping and coordinate choices.
🎗
Mixed — All question types together!
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ROTATION
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