Rotation (clockwise / anti-clockwise 90°)

1Summary 重點摘要

Turn a shape 90° around a point; direction changes.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Three ingredientsDescribing a rotation needs three things made clear: the point it turns around, which is the centre of rotation; the direction, clockwise or anticlockwise; and the angle, such as 90°. Why are all three needed? Because without any one of them the new position of the figure cannot be fixed: without the centre nobody knows which point to turn about; without the direction, clockwise and anticlockwise give different results; without the angle, nobody knows how far to turn. For example, 'rotate the triangle about point O clockwise through 90°' is complete, while 'rotate 90°' alone is not. A common mistake is to leave out the centre or forget the direction; before solving, check that all three ingredients are present, just as an address needs the street, the block and the floor.
2. Step 2: Clockwise 90°Clockwise follows the direction a clock's hands travel. An upward arrow turned clockwise 90° moves like the minute hand from 12 to 3, and afterwards it points right. Remember the order: up becomes right, right becomes down, down becomes left, and left becomes up. Why is the clock the most reliable memory aid? Because everyone knows a clock face: from 12 to 3 is exactly a quarter turn, matching 90°, and picturing the hand walking makes the direction clear at once. For example, the minute hand going from 3 to 6 is likewise a clockwise 90° turn. A common mistake is to confuse the two directions, turning an upward arrow clockwise into pointing left; before judging, draw a small clock face and imagine the hand walking from 12 to 3, and the direction stays straight.
3. Step 3: Anticlockwise 90°Anticlockwise runs against the clock, like a clock played backwards: the same upward arrow turned anticlockwise 90° sends the hand back from 12 to 9, and afterwards it points left. Memorise by contrast: an upward arrow turned clockwise points right, and turned anticlockwise it points left — the two directions give different results and must not be mixed. Why learn the two directions together? Because questions often test both at once, contrast makes the memory firm, and each direction checks the other: the two turns should produce opposite results. For example, a right-pointing arrow turned anticlockwise 90° points up, while clockwise 90° points down. A common mistake is to misread the question, taking anticlockwise for clockwise and getting every direction wrong; before answering, trace the turn once with a pencil tip and confirm it agrees with the question.
4. Step 4: Opposite turns cancelA right-pointing arrow turned clockwise 90° faces down, and a further anticlockwise 90° turn brings it back to the right. Why does it return to the start? Because two 90° turns in opposite directions cancel exactly: what was turned out is turned back, and the figure returns to its original position. This feature serves as a check on rotation results: turn the answer once in the opposite direction, and if it does not recover the original figure, some step in between has gone wrong. For example, an upward arrow turned anticlockwise 90° points left, and a further clockwise 90° should bring it back exactly to up. A common mistake is to think two turns in a row amount to 180°; only when the directions agree do two 90° turns make 180°, while opposite 90° plus 90° amounts to no turn at all — equal angles with opposite directions are what cancel.
5. Step 5: Rotating a whole shapeTurn an L-shape opening right clockwise 90° and the opening faces downward, because every edge of the L turns 90° at the same time — the whole figure rotates together. Why does only the direction change? Because during a rotation every point of the figure turns through the same angle about the same centre, so the distance between any two points never changes; the side lengths, the angles and the size are all preserved, and the rotated figure is exactly the same as the original, only facing differently. For example, a rectangle 3 squares long and 2 squares wide stands 2 long and 3 wide after a 90° turn, yet it is still the same rectangle. A common mistake is to draw the rotated figure distorted, its sides no longer matching; count the squares edge by edge on grid paper to make sure every side keeps its length.
6. Step 6: Check by handHands-on operation is the best verification: press a pencil tip on one corner of the figure as the centre of rotation, turn the paper a quarter turn clockwise, and see where the figure now faces; then turn the opposite way and compare the two results. Why are hands more reliable than imagination? Because rotation is a movement in space, and picturing it in the head easily mixes the directions; turning it yourself shows the difference between clockwise and anticlockwise at a glance, leaving a deep and lasting impression. For example, turn a book clockwise 90° about one corner and then anticlockwise 90°, and watch it return exactly to where it began. A common mistake is to let the pressing finger slide, shifting the centre of rotation and spoiling the result; throughout the turn the tip must stay firmly on the same point — that is the very meaning of the centre.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Describe rotations with centre, direction and angle
• Clockwise follows the clock: up turns 90° to the right
• Anticlockwise runs backwards: up turns 90° to the left
• 90° = a quarter turn = a right angle
• Rotation never changes a shape's size or form