Question
The scale drawing shows two boundaries, AB and BC, of a field ABCD.
The scale of the drawing is 1cm represents 8m.
(a) The boundaries CD and AD of the field are each 72m long.
(i) Work out the length of CD and AD on the scale drawing.
…………………………………… cm
(ii) Using a ruler and compasses only, complete accurately the scale drawing of the field.
(b) A tree in the field is
• equidistant from A and B
and
• equidistant from AB and BC.
On the scale drawing, construct two lines to find the position of the tree.
Use a straight edge and compasses only and leave in your construction arcs
Answer/Explanation
(a)(i) 9
(ii) ABCD completed accurately with arcs
(b) Correct ruled perpendicular bisector of
AB with 2 correct pairs of arcs
Correct ruled bisector of angle ABC with
2 correct pairs of arcs
Lines intersecting
Question
In this question use a ruler and compasses only.
Show all your construction arcs.
The diagram shows a triangular field ABC.
The scale is 1 centimetre represents 50 metres.
(a) Construct the locus of points that are equidistant from A and B.
(b) Construct the locus of points that are equidistant from the lines AB and AC.
(c) The two loci intersect at the point E.
Construct the locus of points that are 250m from E.
(d) Shade any region inside the field ABC that is
• more than 250m from E
and
• closer to AC than to AB.
Answer/Explanation
Ans:
(a) Correct perpendicular bisector of AB
with 2 pairs of correct arcs isw
(b) Correct angle bisector at A with two
pairs of correct arcs isw
(c) Circle centre E radius 5cm isw
(d) 
Question
The boundary of a park is in the shape of a triangle ABC.
AB = 240m, BC = 180m and CA = 140m.
In part (a), show clearly all your construction arcs.
(a) (i) Using a scale of 1 centimetre to represent 20 metres, construct an accurate scale drawing
of triangle ABC. The line AB has already been drawn for you.
(ii) Using a straight edge and compasses only, construct the bisector of angle ACB. Label the point D, where this bisector meets AB.
(iii) Using a straight edge and compasses only, construct the locus of points, inside the triangle, which are equidistant from A and from D.
(iv) Flowers are planted in the park so that they are nearer to AC than to BC and nearer to D than to A. Shade the region inside your triangle which shows where the flowers are planted.
In part (b), use trigonometry.
You must show your working and must NOT use any measurements from your construction in
part (a).
(b) (i) Show clearly that angle ACB is 96.4°.
(ii) Calculate the area of the park.
(iii) Use the sine rule to calculate angle ABC.
▶️Answer/Explanation
(a) (i) Accurate triangle with 2 arcs seen, $2 \mathrm{~mm}$ accuracy for lines $\mathrm{AC}$ and $\mathrm{BC}$
(ii) Accurate bisector of angle $\boldsymbol{A C B}, 2^{\circ}$ accuracy and both pairs of arcs shown (accept equidistant marks on edges for $1^{\text {st }}$ set of arcs) + must meet $A B$
(iii) Accurate perpendicular bisector of AD 2 mm accuracy at mid-point and 2° fo right angle and shows both sets of arcs + must meet AC
(iv) Correct region shaded cao
(b) (i) $(\cos C)=\frac{140^2+180^2-240^2}{2 \times 140 \times 180}$ oe
– 0.111(1)…or better or 96.37 to 96.38
(ii) 0.5 × 140 × 180 sin (their 96.4) oe 12521 to 12523 or 12 500 or 12520 cao www2
(iii) $(\operatorname{Sin} B=) \frac{140 \sin (\text { their } 96.4)}{240}$ oe
35.4 or 35.42 to 35.44 cao www3