Constructions Practice

Transcription

1 1a) In the space below draw a parallelogram. Constructions Practice b) How many lines of symmetry has is got? c) What is the rotational symmetry of a parallelogram? 2. Label this circle correctly Radius Diameter Circumference Chord Arc

2 3. Draw the locus of points 1,5cm away from this line 4. Draw a triangle, using just your compass and a ruler, with sides of length 2cm, 2,5cm and 3cm. You must leave in your construction lines.

3 5. Using only a compass and a ruler, bisect this angle. 6. Draw a line, perpendicular to the line below.

4 7. Draw a shape that is similar to this triangle 8. Show the locus of points 2cm away from this irregular pentagon

5 9. Shade the region that is less than 1,5cm from point C and closer to point B than to point A. A B C 10. Draw the locus of the points that are equal distance from M and N M N

6 11. Draw the locus of the points that are 2cm from point P. P 12. Draw the locus of the points that are 1cm from the line QR Q R

7 13. Sidney patrols the perimeter of a square compound, always walking twenty metres away from the sides of the compound. Draw the locus of the path of Sidney. (Scale: 1 cm to 20 metres) 14. Radio masts are situated at points A, B and C. Signals can be received 60 kilometres from each mast. Shade the region which can receive signals from all three masts. (Scale 1 cm = 40 km) B C A

8 15. A bitch called Ruby and a dog called Shep are tied at points R and S respectively in the garden shown below. Ruby s tether is 6 metres long and Shep s tether is 5 metres long. Show the regions to which they are confined. (Scale 1: 200) R S 16. A ball is rolled so it travels equal distance from two walls, DE and DF. Using a ruler and compasses, construct the locus of the ball. D E F

9 17. The diagram below is a scale drawing of the boundary of a field, into which cows with calves have been introduced. The cattle owner wishes to add an electric fence to discourage the beasts from escaping. The fence is to be two metres within the boundary at all places. (Scale 1: 400) Draw the position of the electric fence. 18. ABCD is a rectangle. Shade the set of points inside the rectangle which are both more than 3 centimetres from point A and more than 1cm from the line DC. A B C D

10 19. Two goats are tethered at points J and K. Salma is trying to walk between the two, keeping an equal distance from each. Show the path that Salma should take. J K 20. The diagram represents a triangular garden ABC. The scale of the diagram is 0,5cm represents 1 m. A tree is to be planted in the garden so that it is nearer to AB than to AC, within 5 m of point A. On the diagram, shade the region where the tree may be planted. B A C

11 You are on a very criminal mission to steal the world famous Loci Diamond. You must enter the room at Door 1, collect the diamond, and exit at Door 2. Sounds simple, but the Loci Diamond is very heavily protected with eight laser beams on the floor. Your challenge is to make a map of the room including the laser beams using the information below then you can figure out a route to take without setting off any alarms. GOOD LUCK! 0,5cm = 1m Laser 1 is always 2.5 metres from the line BD. Laser 2 is equidistant from AB and AC. Laser 2 is beamed from point A. Laser 3 is always 4.5 metres from D. Laser 4 is always 2 metres from post E. Laser 5 is always 1 metre away from the rectangular table F. Laser 6 is 2.5 metres away from the solid wooden bar GH. Laser 7 is equidistant from the statues I and J. Laser 8 is always 2 metres from point K.