Bearings, Scale Drawing, Constructions & Loci Practice Questions

On the map, the distance between Ashwell and Byton is $6.5$ cm.

Work out the real distance, in km, between Ashwell and Byton.

....................................................... km

The real distance between Byton and Carlow is $60$ km.

Work out the distance, in cm, between Byton and Carlow on the map.

....................................................... cm

The diagram shows a van and a lamp post.

The van has a real length of $5$ m.

The van and the lamp post are drawn to the same scale.

Work out an estimate for the real height, $h$ metres, of the lamp post.

....................................................... metres

Write down the bearing of $L$ from $B$ as a three-figure bearing.

.......................................................°

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

.......................................................°

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 lines.

The point $R$ lies on the perpendicular bisector of $AB$.

$RA = 6.5$ cm.

Write down the length of $RB$.

....................................................... cm

Use ruler and compasses to construct the perpendicular from $P$ to the line $l$.

You must show all your construction lines.

The perpendicular from $P$ meets the line $l$ at the point $X$.

Explain why $PX$ is the shortest distance from $P$ to the line $l$.

Use ruler and compasses to construct the bisector of angle $ABC$.

You must show all your construction lines.

The point $T$ is inside angle $ABC$.

$T$ is equidistant from $BA$ and $BC$ and $BT = 6$ cm.

Mark the position of $T$ with a cross ($\times$).

Here is a scale drawing of a rectangular garden $ABCD$.

Scale: 1 cm represents 2 m

Rafi is going to put a bird bath in the garden.

The bird bath must be

• more than $8$ m from the corner $A$
• less than $6$ m from the side $CD$

Show, by shading on the diagram, the region where Rafi can put the bird bath.

A ship sails from $A$ on a bearing of $118°$ for $24$ km to a point $B$.

On the diagram, mark the position of $B$ with a cross ($\times$).

Write down the bearing of $A$ from $B$.

.......................................................°

Complete the scale drawing to show the positions of $B$ and $C$.

Use your scale drawing to work out the real distance, in km, between $A$ and $C$.

....................................................... km

Use your scale drawing to find the bearing of $C$ from $A$.

.......................................................°

Use ruler and compasses to construct triangle $ABC$ accurately.

You must show all your construction lines.

A point $P$ inside triangle $ABC$ is

• nearer to $A$ than to $B$
• less than $4$ cm from $C$

Show, by shading, the region inside the triangle where $P$ could be.

You must show all your construction lines.