Hint
Use the stated units and precision. Subtract the centre, rotate the displacement and add the centre back.
Worked solution
(a)
Subtract the centre, rotate the displacement and add the centre back.
Relative displacement (u,v) becomes (−v,u), so \(\displaystyle x'=-6\).
Answer: \(-6\)
(b)
Use the anticlockwise coordinate order for the relative vector.
The rotated vertical displacement is u, giving \(\displaystyle y'=9\).
Answer: \(9\)
(c)
Use the clockwise rotation rule about the stated centre.
The relative vector becomes (v,−u), so \(\displaystyle x'=2\).
Answer: \(2\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Subtract the centre, rotate the displacement and add the centre back.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Use the anticlockwise coordinate order for the relative vector.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Use the clockwise rotation rule about the stated centre.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.