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Concept 6 of 9

Figure Rotation: Spin to Match

1

Today's big idea

A rotation turns the figure without lifting it, so it never becomes its mirror.

Clockwise runs up, right, down, left, one quarter turn at a time.

2

How it works

👀 What's going on?

A shape is turned rather than flipped, and telling those two apart is most of the battle in this topic.

💡 Here's the trick

90° clockwise: top → rightStart→90° CWAfterRotation quick-facts:90° CW: top → right → bottom → left → top180°: top ↔ bottom · left ↔ right270° CW = 90° anti-clockwiseTip: pin one corner, follow it through.

Look at the arrow above. A rotation turns the whole figure about a point without ever lifting it off the page, so nothing ever becomes its mirror. Tracking one marked part through the turn is enough.

🪄 How to do it

  1. 1.Pick one marked part of the arrow above, such as its tip.
  2. 2.Move that part by the stated angle, in the stated direction.
  3. 3.Redraw the rest of the figure around its new position.

✍️ Try it

An arrow points left. Where does it point after a 90 degree clockwise turn? Then: after 270 degrees clockwise?

Clockwise runs up, right, down, left, so from left a quarter turn reaches up. Three quarter turns from left reaches down.

⚠️ Watch out

You might be thinking a rotation can turn a shape into its mirror image. It cannot. A rotated R is still an R lying at an angle, while a mirrored R is a different shape that no turn will produce.

🌟 Why this matters

Turning a photo the right way up, or fitting a puzzle piece into its slot, is this exact move. Screens rotate this way too, which is why an image never comes back mirrored when you turn your phone.
Exam tip: Say the clockwise order out loud and count quarter turns on your fingers.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“An arrow points UP. Rotate it 90° clockwise. Which way now?”

  1. 1

    Rotation spins, not flips

    Track the arrow tip through a quarter-turn clockwise.

  2. 2

    Apply 90° clockwise

    Up → Right.

  3. 3

    Sanity check

    Another 90° would send it Down, then Left, then back Up.

  4. 4

    Answer ✓

    = Right

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

The arrow points Right. Rotate it 180° clockwise, one quarter-turn at a time.

ROTATION · ROUND 1 OF 3

Pointing: Right

turned 0° of 180°

5

Quick check

✅ VERIFICATION

An arrow points DOWN. Which single turn makes it point LEFT?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Figure Analogy

Quarter turn, half turn or mirror. Say it before you pick.

Concept 7 of 9 →