Bearings, Scale Drawing, Constructions & Loci Practice Questions

On the map, the distance between two churches is $6.8$ cm.

Work out the real distance between the two churches.
Give your answer in km.

The real distance between a school and a railway station is $4.5$ km.

Work out the distance between the school and the railway station on the map.
Give your answer in cm.

Draw a line segment $AB$ of length $8$ cm.

Use ruler and compasses to construct the perpendicular bisector of $AB$.
You must show all your construction arcs.

Draw a straight line and mark a point $P$ on it.

Use ruler and compasses to construct an angle of $60^{\circ}$ at $P$.
You must show all your construction arcs.

Work out the bearing of $A$ from $B$.

Work out the size of angle $ABC$.

Make an accurate scale drawing to show the positions of $A$, $C$ and $D$.
Use a scale of $1$ cm to represent $5$ km.

Use your scale drawing to find the real distance of airport $D$ from airport $A$.
Give your answer in km.

Use your scale drawing to write down the bearing of airport $A$ from airport $D$.

Use ruler and compasses to construct the locus of all the points inside the field that are the same distance from $A$ as they are from $B$.
You must show all your construction arcs.

A water sprinkler is to be placed in the field.
The sprinkler must be

• less than $30$ m from corner $A$
• nearer to $B$ than to $A$

Shade the region in which the sprinkler could be placed.
Label this region $R$.

Make an accurate scale drawing of the field.
Use a scale of $1$ cm to represent $10$ m.

Use your scale drawing to find the real length of $BC$.
Give your answer in metres.

Town $B$ is on a bearing of $055^{\circ}$ from town $A$.
Town $C$ is on a bearing of $145^{\circ}$ from town $A$.
The distance $AB$ is equal to the distance $AC$.

Work out the bearing of $C$ from $B$.
You must show your working.

Make an accurate scale drawing of the field, using a scale of $1$ cm to represent $10$ m.
Draw $BC$ as a horizontal line.

Use ruler and compasses to construct the perpendicular from $A$ to the line $BC$.
You must show all your construction arcs.

Use your construction to find the real perpendicular distance from $A$ to $BC$.

Work out the real area of the field.
Give the units of your answer.