Constructions & loci

Find the straight-line distance from town A to town B.

Give your answer in kilometres.

Find the bearing of town A from town B.

On the map, shade the region containing all the points that are: • closer to town A than to town B, and

• less than 27 km from town B.

The diagram below shows two towns, A and B, on a map.

The scale of the map is 1 cm represents 4·5 km.

On the map, shade the region containing all the points that are: • closer to town A than to town B, and

• less than 27 km from town B.

A B C is a large triangle, where A C = 16 m and B C = 13 m.

Draw a scale drawing of this triangle using the following scale:

1 cm represents 2 m.

The side A B has already been drawn accurately.

What is the size of A C B ?

Point P lies on:

• the bisector of angle A B C • the perpendicular bisector of line B C.

Using only a ruler and a pair of compasses, construct suitable lines and arcs to show the position of point P.

Construction arcs must be clearly shown.

A B C is a large triangle, where A C = 16 m and B C = 13 m.

What is the actual length of A B in the large triangle?

Point P lies on:

• the bisector of angle A B C • the perpendicular bisector of line B C.

Using only a ruler and a pair of compasses, construct suitable lines and arcs to show the position of point P.

Construction arcs must be clearly shown.

Measure and write down the size of angle y.

Draw a line through the point C that is perpendicular to AB.

R is a point on the line LM.

Using only a ruler and a pair of compasses, construct an angle of 90° at point R.

Using only a ruler and a pair of compasses, construct a perpendicular line from the point

P to the line XY.

R is a point on the line LM.

Using only a ruler and a pair of compasses, construct an angle of 90° at point R.

Using only a ruler and a pair of compasses, construct a perpendicular line from the point

P to the line XY.

Triangle ABC is shown in the diagram below.

Using only a ruler and a pair of compasses, construct an accurate drawing of triangle ABC. Side AC has been drawn for you.

All construction lines and arcs must be shown.

Triangle ABC is shown in the diagram below.

Using only a ruler and a pair of compasses, construct an accurate drawing of triangle ABC. Side AC has been drawn for you.

All construction lines and arcs must be shown.

Two sides of a parallelogram ABCD are drawn accurately below. Using only a ruler and a pair of compasses, complete an accurate drawing of the parallelogram.

You must show all your construction arcs.

The line XY below forms part of a scale drawing of a garden. The scale drawing has a scale of 1:200.

What is the actual distance between point X and point Y in the garden?

Give your answer in metres.

Actual distance between point X and point Y =_{……………........ ….…………} metres

Two sides of a parallelogram ABCD are drawn accurately below. Using only a ruler and a pair of compasses, complete an accurate drawing of the parallelogram.

You must show all your construction arcs.

The line XY below forms part of a scale drawing of a garden. The scale drawing has a scale of 1:200.

What is the actual distance between point X and point Y in the garden?

Give your answer in metres.

Actual distance between point X and point Y =_{……………........ ….…………} metres

Using only a ruler and a pair of compasses, construct a triangle PQR, so that it satisfies both of the following conditions: • PQR = 60°, • PQ = 7 cm.

Side QR has been drawn for you.

Using only a ruler and a pair of compasses, construct a line from the point A that is

perpendicular to the line LM.

Using only a ruler and a pair of compasses, construct a line from the point A that is

perpendicular to the line LM.

Draw an accurate scale drawing of the triangle shown above.

Use your scale drawing to calculate the actual length of side BC.

Give your answer in metres.

Actual length of BC =_{………........ ……..} metres

Measure the length of the line AB.

Write your answer in centimetres.

In the space below, draw a circle with a radius of 6 cm.

Measure and write down the size of PQR.

The line AB is drawn below.

The point P lies above the line AB.

The region in which P is located is such that

• P is nearer to point A than to point B,

Using a ruler and a pair of compasses, construct suitable lines and arcs to represent these conditions. Construction arcs must be clearly shown.

Shade the region in which the point P is located.

Use a ruler and a protractor to make an accurate drawing of this triangle.