A point P(2, 3) is mapped onto P(-7, 0) under an enlargement with scale factor of -2. Without drawing, find the centre of enlargement.

Given $P(x, y) = (2, 3)$, $P'(x', y') = (-7, 0)$, and $k = -2$.

$$-7 = a + (-2)(2 - a)$$ $$-7 = a - 4 + 2a$$ $$-7 = 3a - 4$$

$$-7 + 4 = 3a$$ $$-3 = 3a$$ $$a = -1$$

$$0 = b + (-2)(3 - b)$$ $$0 = b - 6 + 2b$$ $$0 = 3b - 6$$

$$6 = 3b$$ $$b = 2$$

The centre of enlargement is $\boxed{(-1, 2)}$.

10. The present age of a father is 10 years more than twice the present age of his son. In how many years time will the age of the father be twice the age of the son.
Let $F$ be the father's current age and $S$ be the son's current age.

"The present age of a father is 10 years more than twice the present age of his son."

$$F = 2S + 10 \quad (1)$$

Let $t$ be the number of years from now when the father's age will be twice the son's age.
In $t$ years, the father's age will be $F+t$.
In $t$ years, the son's age will be $S+t$.
"In how many years time will the age of the father be twice the age of the son."

$$F+t = 2(S+t) \quad (2)$$

$$(2S + 10) + t = 2(S+t)$$ $$2S + 10 + t = 2S + 2t$$

Subtract $2S$ from both sides:

$$10 + t = 2t$$

Subtract $t$ from both sides:

$$10 = t$$

The age of the father will be twice the age of the son in $\boxed{10 \text{ years}}$.

11. A triangular prism ABCDEF with the cross section ABF is such that AB = 3cm, BF = 5.5cm and AF = 4cm. The length of the prism is 6cm. Draw the net of the solid.
As an AI, I cannot physically draw the net. However, I can describe the components and their dimensions, which would allow you to draw it.

A triangular prism consists of two identical triangular bases and three rectangular lateral faces.
The cross-section is triangle ABF, so the two triangular bases are $\triangle ABF$ and $\triangle CDE$.
The dimensions of the triangular bases are:

• Side $AB = 3 \text{ cm}$
• Side $BF = 5.5 \text{ cm}$
• Side $AF = 4 \text{ cm}$

The length of the prism is $6 \text{ cm}$, which is the height of the rectangular faces.
The three rectangular lateral faces are:

• Rectangle $ABCD$: with dimensions $AB \times \text{length of prism} = 3 \text{ cm} \times 6 \text{ cm}$.
• Rectangle $BCFE$: with dimensions $BF \times \text{length of prism} = 5.5 \text{ cm} \times 6 \text{ cm}$.
• Rectangle $AFED$: with dimensions $AF \times \text{length of prism} = 4 \text{ cm} \times 6 \text{ cm}$.

To draw the net, you would typically lay out the three rectangular faces side-by-side, sharing edges. For example, you could place the $3 \text{ cm} \times 6 \text{ cm}$ rectangle, then attach the $5.5 \text{ cm} \times 6 \text{ cm}$ rectangle to its $6 \text{ cm}$ side, and then attach the $4 \text{ cm} \times 6 \text{ cm}$ rectangle to the $6 \text{ cm}$ side of the second rectangle. Finally, attach the two triangular bases (with sides $3 \text{ cm}$, $5.5 \text{ cm}$, $4 \text{ cm}$) to the $3 \text{ cm}$ side of the first rectangle and the $4 \text{ cm}$ side of the third rectangle, respectively.