The point C lies on the line AB such AC:AB = 2:7.

1. Express $BC$ in ratio parts and form the fraction $\dfrac{AC}{BC}$.

Since $AC:AB=2:7$, let $AC=2$ parts and $AB=7$ parts.

As $C$ lies on $AB$,
$BC=AB-AC=7-2=5\text{ parts}.$

Hence,
$AC \text{ as a fraction of } BC=\frac{AC}{BC}=\frac{2}{5}.$

1. Find the number of ratio parts represented by $BC$ and scale using $AC=24$ cm.

Since $AC:AB=2:7$,
$BC=AB-AC=7-2=5\text{ parts}.$
$AC=2$ parts $=24$ cm, so
$1\text{ part}=12\text{ cm}.$
Hence
$BC=5\times 12=60\text{ cm}.$