18.3 Enlargement with fractional and negative scale factors — Practise

1. Enlarge $(6,-4)$ by scale factor $1/2$ about the origin.

Answer: (3,-2)

2. Enlarge $(2,3)$ by scale factor $-2$ about the origin.

Answer: (-4,-6)

3. Enlarge $(-8,4)$ by scale factor $-1/2$ about the origin.

Answer: (4,-2)

4. Triangle vertices are $(2,0),(0,4),(2,4)$. Enlarge by factor $-1/2$ about the origin.

Answer: (-1,0), (0,-2), (-1,-2)

5. A length of $12$ cm maps to $3$ cm. Give the positive scale factor.

Answer: 1/4

6. Point $(-3,5)$ maps to $(6,-10)$. Give the scale factor for an enlargement centred at the origin.

Answer: -2

7. Point $(4,0)$ maps to $(-2,0)$ under an enlargement centred at the origin. Find the scale factor.

Answer: -1/2

8. Explain what the negative sign in scale factor $-3$ tells you.

Answer: The image is on the opposite side of the centre; lengths are tripled.

9. Enlarge $(12,8)$ by scale factor $-1/4$ about the origin.

Answer: (-3,-2)

10. Which method maps $(4,6)$ to $(2,3)$ about the origin: translation or enlargement? Give a reason.

Answer: Enlargement, scale factor $1/2$, because both coordinates are multiplied by the same number.