20 The scale diagram below shows towns, A, B and C. Line AB represents the road from A to B and line AC represents the road from A to C.
A shopping centre is to be built so that it is
nearer to the road from A to B than the road from A to C,
less than 14 km from town C.
(a) Using construction, shade the region where the shopping centre could be built. Show all your construction lines.
[5]
(b) Explain why the region found in part (a) may not be an appropriate site for the shopping centre. [1]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Accurate angle bisector with 2 pairs of correct arcs
2
B1 for correct bisector with no arcs or incorrect arcs
The bisector does not have to go through A but if extended it must go through A and it must lie within green lines in overlay. For 2 marks condone intersecting arcs of equal radius, one centre B and the other centre C for the construction with bisector drawn.
Arc centre C radius 7cm
2
B1 for arc centre C with incorrect radius
For arc, measure radius using ruler.
tolerance \(\pm\) 2 mm and \(\pm\) 2° for both constructions
Correct region indicated
1Dep
Dependent on at least B1 for bisector and B2 for arc
Mark scheme (b)
Answer
Marks
Part marks and guidance
accept any correct assumption e.g. Road[s] is not/are not straight, road AB is busier than road AC, land is not suitable for construction
1
If more than one choose the best one see list of exemplars
