Mathematics 4024 · O Level · Geometrical constructions

Geometrical constructions — practice question

The diagram displays a field, $ABCD$, drawn at a scale of $1\text{ cm}$ to $50\text{ m}$.
(a)[2]

A straight path runs from $D$ to the midpoint of $AB$ across the field. Draw this path and measure the angle it makes with $DC$.

(b)[4]

Grass will be planted in part of the field. This area must be less than $325\text{ m}$ from $B$, must lie closer to $CB$ than to $CD$, and may be placed only on one side of the path. Use suitable loci to determine and shade the greatest possible grassy area.

(c)[1]

Calculate the real length of the section of the path that acts as a boundary for the grass.

Worked solution & mark scheme

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