Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to rotate a point through a quarter-turn.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Coordinate quadrants and square roots.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
Rotate P(2,5) by 90° counterclockwise about the origin. Find its image and check its distance from the centre.
Why this math matters
A quarter-turn about the origin exchanges coordinate roles with a sign determined by the rotation direction. Track where a familiar axis point moves to check a rotation rule's direction.
Set up the model
A useful answer starts with clear assumptions:
- Positive angles mean counterclockwise rotation.
- The rotation centre is the origin.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Rotate a point through a quarter-turn
PausedQuestion: Start with the question. Paused.
Question
Start with the question
Rotate P(2,5) by 90° counterclockwise about the origin. Find its image and check its distance from the centre.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
90° counterclockwise rule: (x,y) → (−y,x)
The positive x-axis rotates to the positive y-axis, fixing the direction of the rule.
Apply the relationship
P(2,5) → P′(−5,2)
The point moves from quadrant I to quadrant II.
Check and interpret
OP = √29 and OP′ = √29
Both squared distances are 2² + 5², so the rotation preserves distance from the centre.
The result
OP = √29 and OP′ = √29
Both squared distances are 2² + 5², so the rotation preserves distance from the centre.
Common mistakes to catch
- Clockwise and counterclockwise quarter-turns require different signs.
- Origin-based formulas cannot be used unchanged for a different rotation centre.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Rotate (3,−1) by 90° clockwise about the origin.
Show a hint
The clockwise rule is (x,y) → (y,−x).
Reveal answer and explanation
(−1,−3)
Apply the clockwise rule to get (−1,−3).
Practice 2
Rotate (−4,6) by 180° about the origin.
Show a hint
A half-turn reverses both coordinate directions.
Reveal answer and explanation
(4,−6)
The rule is (x,y) → (−x,−y).
Take the idea with you
Track where a familiar axis point moves to check a rotation rule's direction.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Connect dilation with length and area factors
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