Hint
Use the stated units and precision. Divide image length by its corresponding original length.
Worked solution
(a)
Divide image length by its corresponding original length.
The corresponding ratio \(\displaystyle \frac{DE}{A}B\) is \(\displaystyle \frac{9}{2}\).
Answer: \(\displaystyle \frac{9}{2}\)
(b)
Use correspondence in the stated vertex order.
Multiply BC by the same scale factor to obtain \(\displaystyle \frac{81}{2}\) cm.
Answer: \(\displaystyle \frac{81}{2}\)
(c)
Apply the length scale to the entire perimeter.
Every side scales by \(\displaystyle \frac{9}{2}\), so the perimeter becomes \(\displaystyle \frac{189}{2}\) cm.
Answer: \(\displaystyle \frac{189}{2}\)
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: Divide image length by its corresponding original length.
- 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 correspondence in the stated vertex order.
- 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: Apply the length scale to the entire perimeter.
- 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.