Constructions & loci

Construct the region that lies within 4 cm of the line.

Measure the shortest distance from point P to the line. Give your answer in millimetres.

Use a ruler and compasses in this question.

The scale diagram shows port P and lighthouse Q.

Scale: 1 cm represents 2 km

A ship is less than 14 km from P and closer to Q than to P.

Label the region, R, where the ship could be. Show all your construction lines.

Use a ruler and compasses in this question. ABCD represents a garden.

A tree is to be planted in the garden. The tree will be in the region that is closer to AB than to BC. Label the region, R, where the tree could be planted. Show all your construction lines.

Use a ruler and compasses in this question. ABCD represents a garden.

A tree is to be planted in the garden. The tree will be in the region that is closer to AB than to BC. Label the region, R, where the tree could be planted. Show all your construction lines.

Towns A and B are shown on a centimetre grid.

What does the shaded area represent? Tick one box.

Complete an accurate drawing of triangle PQR so that angle QPR is 53 ° the length of side PR is 7.5 cm

ABCD represents the plan of a field.

There is a path across the field that starts at B is the same distance from BA and BC. Using ruler and compasses, show the position of the path.

ABCD represents the plan of a field.

There is a path across the field that starts at B is the same distance from BA and BC. Using ruler and compasses, show the position of the path.

An equilateral triangle has side length 16 metres. Using ruler and compasses only, construct a scale drawing of the triangle. Use the scale 1 centimetre represents 2 metres.

Scale: 1 cm represents 2 m

An equilateral triangle has side length 16 metres. Using ruler and compasses only, construct a scale drawing of the triangle. Use the scale 1 centimetre represents 2 metres. Scale: 1 cm represents 2 m

Using ruler and compasses, show the region inside the grid that is less than 4 cm from A and nearer to B than to C. Label the region R. Show all your construction lines.

Using ruler and compasses, show the region inside the grid that is less than 4 cm from A and nearer to B than to C. Label the region R. Show all your construction lines.

The scale drawing represents a garden. Water from a sprinkler at P reaches up to 20 metres from P. Water from a sprinkler at Q reaches up to 25 metres from Q. Scale: 1 cm represents 5 m

Using a pair of compasses, show the region that water from both sprinklers reaches.

A sketch of triangle ABC is shown.

In the space below, complete an accurate drawing of triangle ABC.

Joe wants to bisect angle BCD.

Here is his method. Use a pair of compasses to draw arcs of the same radius from B and D. Draw a straight line from C through the intersection of the arcs.

Write down the error in his method.

Kay wants to show all the points 3 km from point P. Scale: 1 cm represents 1 km

× P

Here is her answer. Scale: 1 cm represents 1 km

What is wrong with her answer?

Here is a rectangle.

Using a pair of compasses and a straight edge, construct one line of symmetry. Show clearly your construction arcs.

Construct a locus of points that are the same distance from points A and B.