Constructions & loci

The point C is shown on a centimetre grid.

A point P is at least 2 cm from the point C. Nadia is asked to shade the region where point P could be. Her answer is shown on the grid. Explain the mistake Nadia has made.

The point C is shown on a centimetre grid.

A point P is at least 2 cm from the point C. Nadia is asked to shade the region where point P could be. Her answer is shown on the grid. Explain the mistake Nadia has made.

Use ruler and compasses to construct the bisector of angle ABC. You must show your construction lines.

Use ruler and compasses to construct the bisector of angle ABC. You must show your construction lines.

Here is a triangle ABC.

The region R consists of all points inside the triangle that are less than 4 cm from A and closer to C than to B. On the diagram show, by shading, the region R.

The point P lies on the line AB. Use ruler and compasses to construct an angle of 90 at P. You must show all your construction lines.

The point P lies on the line AB. Use ruler and compasses to construct an angle of 90 at P. You must show all your construction lines.

Draw accurately an isosceles triangle with sides of length 8 cm, 6 cm and 6 cm. One side of the triangle has been drawn for you.

8 cm

Use a ruler and compasses to construct the line from the point P perpendicular to the line CD. You must show all construction lines.

Use a ruler and compasses to construct the line from the point P perpendicular to the line CD. You must show all construction lines.

Here is a plan of a kitchen drawn to a scale of 1: 30

A B

Sam is going to put a small table in the kitchen. The table has to be more than 180 cm from A more than 150 cm from BC Show, by shading on the diagram, the region where Sam can put the table.