Constructions and Scale Drawings — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)Real distance (cm) = map distance × scale factor, then convert cm to km (÷100 000).
3.4 × 50 000 = 170 000 cm = 1.7 km
Question 2
(a)A perpendicular bisector is constructed using arcs from each end of the line.
A pair of compasses, a ruler, and a pencil
Question 3
(a)Real 8 m = 800 cm; divide by the scale factor 200.
800 ÷ 200 = 4 cm
Question 4
(a)The reverse bearing is found by adding 180° (or subtracting if over 180°).
70 + 180 = 250°
Question 5
(a)Draw a line, then from one end draw an arc crossing the line. From that crossing point, draw another arc of the same radius crossing the first arc — the angle from the original point to this new intersection is 60°, since an equilateral triangle has been constructed.
Construct an equilateral triangle using two equal-radius arcs — each of its angles is 60°
Question 6
(a)Use trigonometry: east distance = 40 × sin(135°), north distance = 40 × cos(135°) (with north component negative here, since 135° is south-east of due north).
East/north components found using distance × sin(bearing) and distance × cos(bearing)
Question 7
(a)Multiply by scale factor 1000, then convert cm to m (÷100).
2.5 × 1000 = 2500 cm = 25 m
Question 8
(a)Subtract 180° when the bearing is over 180°.
210 − 180 = 30°
Question 9
(a)This is the definition of a perpendicular bisector.
The perpendicular bisector of the line segment AB
Question 10
(a)A pair of compasses and a straight edge (ruler) are sufficient.
A pair of compasses and a ruler/straight edge
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