Find the distance from ${\text{P}}(100,{\text{ }}200)$ to ${\text{A}}$. Give your answer correct to two decimal places.

Write down your answer to part (a) correct to three significant figures.

Write down your answer to part (b) in the form $a \times {10^k}$, where $1 \leqslant a < 10$ and $k \in \mathbb{Z}$.

$\sqrt {{{(100 - 1)}^2} + {{(200 + 2)}^2}}$     (M1)

$\sqrt {50605} \;\;\;( = 224.955 \ldots )$     (A1)

Note: Award (M1)(A1) if $\sqrt {50605}$ seen.

${\text{224.96}}$     (A1)     (C3)

Note: Award (A1) for their answer given correct to 2 decimal places.

$225$     (A1)(ft)     (C1)

Note: Follow through from their part (a).

$2.25 \times {10^2}$     (A1)(ft)(A1)(ft)     (C2)

Notes: Award (A1)(A0) for $2.25$ and an incorrect index value.

Award (A0)(A0) for answers such as $22.5 \times {10^1}$.