WAEC Mathematics 2013 Theory — Question 10

Model answer

(a) Construction procedure: (i) Draw a straight line across the page, choose a suitable point W and locate a 10.2cm point away from W on the same straight line; mark the new point as X. (ii) Construct angle 60° at X using a ruler or compass; locate point Y, 5.6cm from X on the line drawn at 60° from X. (iii) Using the straight line |XY| as base, construct another angle 60° from Y, draw a straight line parallel to |WX|. (iv) Locate a point Z, 5.8cm on the line drawn from Y to W, to form your trapezium. (v) To construct a perpendicular line from Z: using point Z as base point, construct angle 90°; this forms a perpendicular line. (Alternatively: using point Z as centre, draw an arc to cut |WX| at any two points, bisecting the line joining these two points would give the required perpendicular from Z to |WX|.) (vi) Measure |WZ| and |ZN|. (b) By construction and measurement: (i) |WZ| ≈ 6.2cm (measured from the accurately constructed diagram); (ii) |ZN| ≈ 5.0cm (measured perpendicular distance).