(a) Using only a ruler and a pair of compasses, construct a triangle PQR, so that it satisfies both of the following conditions:
\(P\hat{Q}R = 60^\circ\),
PQ = 7 cm.
Side QR has been drawn for you. [2]
On screen this diagram may not be shown at actual size. To measure it, use the question paper (PDF) printed at 100%.
(b) Using only a ruler and a pair of compasses, construct a line from the point A that is perpendicular to the line LM. [2]
Mark scheme (a)
Scheme
Marks
Comments
Correct construction of angle PQR = 60°.
M1
Correct construction arcs must be seen and angle drawn.
Correct triangle PQR drawn,
A1
PQ = 7 cm (±2mm) and triangle drawn. Allow non labelling of point P (unless position contradicted). Ignore extension of line QP if correct triangle drawn.
Mark scheme (b)
Scheme
Marks
Comments
Arc, centre A, intersecting LM at two points AND Intersecting arcs (equal radii) using the above two points as centres.
M1
[Note to markers: These arcs may be identified by the fact that they will ‘cross the line LM at an acute angle’. Arcs ‘crossing the line at 90°’ is evidence of an inappropriate method.]
Line drawn
A1
Alternative method.
Scheme
Marks
Comments
Using the properties of a kite. Intersecting arcs whose centres are any two points on the line LM and respective radii equal in length to the distance from the points to the point A.
M1
[Note to markers: The arcs will always intersect at a point that is a ‘reflection of point A’ in the line LM.]
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