(a) Construct the perpendicular from the point P to the line AB.
[2]
(b) The diagram shows a field LMN.
A tree is to be planted in the field so that it is
the same distance from the fences MN and ML
and
the same distance from corner M as from corner N.
Show, by construction, whether this can be done or cannot be done.
This .................... be done. [5]
Mark scheme (a)
Answer
Marks
Part marks and guidance
Ruled line through P and perpendicular to AB constructed with correct arcs (one pair intersecting AB)
2
B1 for correct arcs (one pair intersecting AB) only but no line or correct ruled line but no, or incomplete, construction arcs
Condone dotted lines Set protractor to 90° and check 88° to 92° at AB
Correct construction arcs as shown (may be two pairs of arcs used to draw line through P) Ignore other arcs if correct arcs clearly used to construct line
Condone perpendicular extending beyond AB but must pass through P and reach AB (no daylight)
Alternative arcs (eg a kite construction) One centred on A length AP and one centred on B length BP meeting below AB (may also pass through P). Candidates may use points on AB other than A and B for this construction. In such cases check radii of arcs using on-line ruler to judge
See appendix for exemplars (marked diagrams in the published mark scheme)
Mark scheme (b)
Answer
Marks
Part marks and guidance
accurate and correct ruled angle bisector of angle M with supporting arcs and accurate and correct ruled perpendicular bisector of MN with supporting arcs and ‘cannot’ with full evidence
5
B2 for accurate and correct ruled angle bisector of angle M with supporting arcs or B1 for accurate and correct ruled angle bisector of angle M
B2 for accurate and correct ruled perpendicular bisector of MN with supporting arcs or B1 for accurate and correct ruled perpendicular bisector of MN
B1 dep for correct decision (No) with full evidence dep on at least B1 B1
tolerance on angles \(\pm\) 2° and on radius of arcs \(\pm\) 2mm
For 5 marks the diagram must be fully correct with no extra constructions and lines touching the opposite sides of the triangle.
Bisectors to be at least 2cm long
full evidence means two correct ruled lines within tolerance
