# Applied geometry-scale drawing and bearing Questions and Answers

Form 1 Mathematics: Applied geometry-scale drawing and bearing Questions and Answers

Lessons (**19**) * SHARE*

- 1.
A town P is 200km west of Q. Town R is at a distance of 80km on a bearing of #049^0# from P. Town S is due east of R and due North of Q. Determine the bearing of S from P.

11m 14s - 2.
A route for a safari rally has five sections AB, BC, CD, DE and EA. B is 200km on a bearing #050^0# from A. C is
500km from B. The bearing of B from C is #300^0#. D is 400km on a bearing of #230^0# from C. E is 250km on a bearing #025^0# from D. Using the scale 1 cm for 50km draw the diagram representing the route for the rally. From the diagram determine
(i) the distance in km of A from E
(ii)

24m 26s - 3.
Manyatta village is 74 km North West of Nyangate village. Chamwe village is 42 km west of Nyangate. By using an appropriate scale drawing, find the bearing of Chamwe from Manyatta

9m 58s - 4.
A port B is on a bearing of #080^0# from a port A and at a distance of 95 km. A submarine is stationed at a port D, which is on a bearing of #200^0# from A and a distance of 124 km from B. A ship leaves B and moves directly
southwards to an island P, which is on a bearing of #140^0# from A. The submarine at D on realizing that the ship was heading for the island P, decides to head straight for the

21m 49s - 5.
Four towns R, T, K and G are such that T is 84 km directly to the north R, and K is on a bearing of #295^0# from R at a distance of 60 km. G is on a bearing of #340^0# from K and a distance of 30 km. Using a scale of 1 cm to represent 10 km, make an accurate scale drawing to show the relative positions of the town. Find
(a) The distance and the bearing of T from K
(b) The distance and the bearing

14m 16s - 6.
Two airplanes S and T leaves an airport at the same time. S flies on a bearing of #060^0# at 750 km/ h while T
flies on a bearing of #210^0# at 900km/h.
(a) Using a scale draw a diagram to show the positions of the airplanes after 2 hours.
(b) Use the diagram to determine
(i) the actual distance between two airplanes
(ii) The bearing of T from S
(iii) The bearing of S from T

12m 2s - 7.
Two airplanes P and Q leaves an airport at the same time. P lies on a bearing of #240^0# at 900 km/ h while Q
flies due east at 750 km/ h.
(a) Using a scale of 1 cm to represents 100km, make a scale drawing to show the position of the airplanes after 40 minutes.
(b) Use the scale drawing to find the distance between the two airplanes after 40 minutes.
(c) Determine the bearing
(i) P from Q
(ii) Q

10m 32s - 8.
Four points B, C,Q and D lie on the same plane. Point B is 42km due south –west of point Q. Point C is 50km on a
bearing of #S60^0E# from Q. Point D is equidistant B, Q and C.
a) Using the scale: 1cm represents 10km,construct a diagram showing the positions of B, C, Q and D.
b) Determines the:
i) Distance between B and C
ii) Bearing of D from B.

11m 55s - 9.
A ship leaves port p for port R though port Q.Q is 200 km on a bearing of #220^0# from P.R is 420 km on the bearing of #140^0# from Q.
a) Using the scale 1:4,000,000, draw a diagram, showing the relative positions of the three ports P, Q, and R.
b) By further drawing on the same diagram, determine how far R is to the east of p
c) If the ship has sailed directly from P to R at an average speed of

14m 5s - 10.
Four electricity posts, A,B,C, and D stand on a level ground such that B is 21m on a bearing of #060^0# from A, C, is 15 m to the south of B and D is 12 m on a bearing of #140^0# from A.
(a) (i) Using scale of 1 cm of I cm to represents 3 metres, draw a diagram to show the relative positions of the posts
(ii) Find the distances and the bearing of C from D
(b) The height of the post at A is 8.4m. O

13m 14s - 11.
Three points P, Q and R are on a level ground. Q is 240 m from P on a bearing of #230^0#. R is 120 m to the east of P. a) Using a scale of 1 cm to represent 40 m, draw a diagram to show the positions of P, Q and R
b) Determine
i) The distance of R from Q
ii) The bearing of R from Q
c) A vertical post stands at P and another one at Q. A bird takes 18seconds to fly directly from the top of the
post

11m 46s - 12.
The boundaries PQ, QR, RS and SP of ranch are straight lines such that: Q is 16km on a bearing of #040^0# from P, R is directly south of Q and east of P and S is 12km on a bearing of #120^0# from R.
(a) Using a scale of 1cm represent 2km, show the above information in a scale drawing.
(b) From the scale drawing determine
(i) The distance, in kilometers of P and S
(ii) The bearing of P from S
(c)

14m 48s - 13.
Three police posts X, Y and Z are such that Y is 50 km on a bearing of 060° from X while Z is 70 km from Y and on a bearing of 300° from X.
(a) Using a suitable scale, draw a diagram to represent the above situation.
(b) Determine the distance, in km, of Z from X.

7m 23s - 14.
Three pegs R, S and T are on the vertices of a triangular plain field. R is 300 m from S on a bearing of 300° and T is 450 m directly south of R.
(a) Using a scale of 1 cm to represent 60 m, draw a diagram to show the positions of the pegs.
(b) Use the scale drawing to determine:
(i) The distance between T and S inmetres
(ii) The bearing of T from S.
(c) Find the area of the field, in hectares, c

9m 54s - 15.
A plane leaves an airstrip L and flies on a bearing of 040° to airstrip M, 500km away. The plane then flies on a bearing of 316° to airstrip N. The bearing of N from L is 350°. By scale drawing, determine the distance between airstrips M and N.

7m 27s - 16.
The corner points A, B, C and D of a ranch are such that B is 8km directly East of A and C is 6km from B on a
bearing of 30°. D is 7km from C on a bearing of 300°.
(a) Using a scale of 1cm to represent 1km, draw a diagram to show the positions of A, B, C and D.
(b) Use the scale drawing to determine:
(i) The bearing of A from D
(ii) The distance BD in kilometers.

8m 36s - 17.
(a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle.
(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres.

12m 48s - 18.
Three villages A, B and C are Such that B is 53 km on a bearing of 295° from A and C is 75 km east of B.
(a) Using a scale of 1
cm to represent 10 km,
draw a diagram to show the relative positions of villages A, B and C.
(b) Determine the distance, in km, of C from A.

5m 3s - 19.
Using a ruler and a pair of compass only, construct a rhombus PQRS such that PQ = 6cm and

9m 53s

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