Mathematics 0580 · IGCSE · Geometrical constructions

Geometrical constructions — practice question

The scale drawing depicts a park, $ABCDE$. The scale is 1 centimetre represents 20 metres. North is indicated.
(a)[1]

Measure the bearing from $A$ to $B$.

(b(i))[2]

Construct the line of the cycle path.

(b(ii))[2]

Find the actual length, in metres, of the cycle path.

(b(iii)(a))[1]

Show that 9 km/h can be written as $2.5\ \text{m s}^{-1}$.

(b(iii)(b))[2]

Work out how long she takes to cycle from $E$ to $BC$. Give your answer in seconds.

(c)[2]

Construct the straight footpath.

(d(i))[2]

Construct the locus of points that are 150 metres from $A$ and lie inside the park.

(d(ii))[1]

A region for sports activities is less than 150 metres from $A$ and nearer to $E$ than to $D$. Shade this region.

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