Start with the base AB = 6.5 cm. Then open the pair of compasses to 5 cm … · 2014-10-13 · 4 Construct an equilateral triangle with sides of length 4.5 cm. Guided practice worksheet

313A

Guided practice worksheet

�3 14.1 Constructing triangles

1 Here is a sketch of triangle ABC.

Construct an accurate drawing of triangle ABC.

2 Here is a sketch of triangle XYZ.

Construct an accurate drawing of triangle XYZ.

6.5 cm

7 cm

C

A B

5 cm

3 cm

4 cm

Z

Y X

5 cm

Start with the base AB = 6.5 cm. Then open the pair of compasses to 5 cm and draw an arc, centre A.

Questions are targeted at the grades indicated

D


313B

3 Here is a sketch of the triangle PQR.

Construct an accurate drawing of the triangle PQR.

4 Construct an equilateral triangle with sides of length 4.5 cm.


Hint It is a good idea to draw a sketch � rst.

8 cm5cm

5cmP Q

R

D


313C

5 Construct the triangle ABC with sides AB = 4.5 cm, BC = 5.5 cm and CA = 5.5 cm.

6 Construct the triangle PQR with sides PQ = 4.8 cm, QR = 5.8 cm and RP = 6.8 cm.


D


313D

7 Construct triangle XYZ with sides XY = 4.0 cm, YZ = 5.8 cm and ZX = 7.1 cm.

8 Here is a sketch of the quadrilateral CDEF.

Make an accurate drawing of quadrilateral CDEF.


3.2 cm

4.5 cm

5.5 cm4 cm

6.4 cm

E

DC

F

D

�3 14.2 Perpendicular lines

315A

1 Construct the perpendicular bisector of each of the lines AB.

2 Construct the perpendicular bisector of each of the lines XY.


Draw arcs above and below the line to be bisected.

A B

A B

A B

A B

A B

A B

A B

A B

A B

X Y

X

Y

X

Y

X Y

X

Y

X

Y

X Y

X

Y

X

Y

C



315B

3 Construct the perpendicular from the point P on the line AB in each of the following cases.

4 Construct the perpendicular from the point P to the line AB in each of the following cases.


A BP

B

P

A

A

P

B

A

A

B

B

P

A

B

P P

A

A

B

B

P

A

B

P P

Remember to start by drawing arcs, centre P, which cut AB on either side of P.

Remember to draw arcs, centre P, to cut AB.

C


315C

5 Construct the perpendicular from P to the side QR of the triangle PQR in each case.


Q

P R Q R

P

C

�3 14.3 Constructing and bisecting angles

317

1 In each case, construct the bisector of the angle ABC. Remember to start by drawing arcs centre B to cut BA and BC.

A

B C

C

C

B

B

B

C

A

A

A

A

B C

C

C

B

B

B

C

A

A

A


C


A

B C

C

C

B

B

B

C

A

A

A

A

B C

C

C

B

B

B

C

A

A

A

�3 14.4 Loci

319A

1 Draw the locus of all points that are equidistant from X and Y.

2 Draw the locus of all points that are equidistant from C and D.

3 Draw the locus of all points that are 1.5 cm from the point P.

4 Draw the locus of all points that are 3 cm from the line segment AB.


X Y

C

D

A B

P ×

Think what property the perpendicular bisector of XY has.

Hint Think about the shape this will produce.

Remember to think carefully about what happens at the ends, A and B

C


�3 14.4 Loci

319B

5 Draw the locus of all points that are equidistant from the lines PQ and PR.


P

R

Q

C

�3 14.5 Regions

321A

1 Shade the region of points that are less than 2.5 cm from the point P.

2 Shade the region of points less than 1.8 cm from the line segment AB.

3 Shade the region of points closer to C than D.

4 Shade the region of points closer to the line AB than to the line AC.


P ×

A B

C ×

D ×

A C

B

Think carefully about what to do about the points A and B.

C


�3 14.5 Regions

321B

5 Show, by shading, the region of points more than 1.6 cm from the point Q.


Q ×

C

�3 14.6 Bearings

323A

1 Measure and write down the bearing of B from A.

a b c d e

.................................. .................................. .................................. .................................. ..................................

2 Use the protractor to draw diagrams of the following bearings.

a The bearing from A to B is 075°. b The bearing of C to D is 210°.

c The bearing from E to F is 148°.

N

A

B

N

A

B

N

A

B

N

A

N

B

NN

B

A

N

A

B

N

A

B

N

A

B

N

A

N

B

NN

B

A

N

A

B

N

A

B

N

A

B

N

A

N

B

NN

B

A

N

A

B

N

A

B

N

A

B

N

A

N

B

NN

B

A

N

A

B

N

A

B

N

A

B

N

A

N

B

NN

B

A

Guided practice worksheet Questions are targeted at the grades indicated

�3 14.6 Bearings

323B

3 The bearing of x from y is 067°. Work out the bearing of y from x.

..............................................................................................................................

4 The bearing of Heathrow airport from a plane is 237°.

Work out the bearing of the plane from Heathrow airport.

..............................................................................................................................

5 The bearing of a lighthouse from ship A is 307°. The ship is 5 km from the lighthouse. The bearing of a second ship B from ship A is 270°. Ships A and B are 4 km apart.

a Draw a scale diagram showing the positions of the two ships.

b How far away from the lighthouse is ship B?

.....................................................................................................

6 A boat leaves a port on a bearing of 069°.

Work out the bearing the boat needs to use to return to port.

..............................................................................................................................


D

Hint Use a scale of 1 cm = 1 km

�3 14.7 Scale drawings and maps

325A

1 The Eiffel tower is 324 m high. A model has a scale of 1 : 400. Calculate its height.

.....................................................................................................................................................................................................................................

2 A map has a scale of 1 : 50 000. Karen measured the following distances on the map. What are the distances in the real world, in km?

a Snedbury to Fley 9 cm

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

b St John’s Church to Kipley Cross 2.5 cm

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

c Draybridge to Gleet 29 cm

.................................................................................................................................................................................................................................

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d Bridge to Weir 17 mm

.................................................................................................................................................................................................................................

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3 A central London map has a scale of 1 : 11 500. Find the distance on the map, in cm, for each real distance given below. Work to the nearest mm.

a Piccadilly Circus to Parliament Square 1.9 km ..............................................................................................................................

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

b Marble Arch to Hyde Park Corner 2.07 km .......................................................................................................................................

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................


Newton to Crotchley 12 cm Real world distance = 50 000 × 12 cm = 600 000 cm = 6 km

D

Trafalgar Square to To� enham Court Road 1.5 km 1.5 km = 1.5 × 1000 m = 150 000 cm Map distance = 150 000 cm ÷ 11 500 = 13.0 cm (to nearest mm)



325B


c British Library to Oxford Circus 1.84 km ............................................................................................................................................

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

d Covent Garden to Leicester Square 520 m .......................................................................................................................................

.................................................................................................................................................................................................................................

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4 The body of a Chinook helicopter is 52.1 m long. A scale model is 20.8 cm long.

a Find the ratio of the scale model in the form 1 : n

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

b The rotor blade length is 30.2 m. Find the width of the model, to the nearest mm.

.................................................................................................................................................................................................................................

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5 This Pearson logo was enlarged so that its length was 1.7 m.

a Find the scale of the enlargement in the form 1 : n

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

b Find the height of the enlargement, to the nearest cm.

.................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................

D

C


325C


6 This map of the Isle of Wight has a scale of 1 : 500 000

i Measure the distance between the two towns, in cm, to 1 decimal place.

ii Calculate the real distance between the towns, in km.

a Cowes to Ryde i .................................................................. ii ..................................................................

b Ryde to Sandown i ................................................................. ii ..................................................................

c Sandown to Shanklin i .................................................................. ii ..................................................................

d Newport to Freshwater i ................................................................. ii ..................................................................

e Freshwater to Ventnor i .................................................................. ii ..................................................................

f Ventnor to Cowes i .................................................................. ii ..................................................................

g Bembridge to Freshwater i .................................................................. ii ..................................................................

h Sandown to Ventnor i .................................................................. ii ..................................................................

7 This is a plan of an art gallery.

a The East wall has a real length of 12 m. Find the scale of the map in the form

i 1 cm represents n m ..................................................................................................................................................................................

ii 1 : n ............................................................................................................................................

C

Eastwall

Freshwater

Northwood

Cowes

Ryde

Seaview

Bembridge

Sandown

Shanklin

Ventnor

Newport

D


325D


b Draw an accurate scale drawing on centimetre squared paper. C

Documents

Start with the base AB = 6.5 cm. Then open the pair of compasses to 5 cm … · 2014-10-13 · 4 Construct an equilateral triangle with sides of length 4.5 cm. Guided practice worksheet