(a) Line AB is shown below. Using only a ruler and a pair of compasses, construct an angle of 60° at point B. [1]
(b)R is a point on the line LM. Using only a ruler and a pair of compasses, construct an angle of 90° at point R. [1]
(c) Using only a ruler and a pair of compasses, construct a perpendicular line from the point P to the line XY. [2]
Mark scheme (a)
Scheme
Marks
Comments
Correct construction of 60°
B1
Must be at point B. Correct construction arcs (two or three) must be seen (initial and secondary). B0 if 60° and 30° drawn. Ignore additional lines provided intended 60° is clear (e.g any triangle, including equilateral ABC). For example:
In the original the labels and arrows in the example (‘secondary arc’, ‘inital arcs’) are in red.
Mark scheme (b)
Scheme
Marks
Comments
Correct construction of 90°
B1
Must be at point R above or below LM. Correct construction arcs (initial and secondary) must be seen.
Mark scheme (c)
Scheme
Marks
Comments
All correct construction arcs shown
M1
Arc, centre P, intersecting XY at two points. (X may be one of the points with no arc seen at point X) [Note to markers: These arcs may be identified by the fact that they will ‘cross the line XY at an acute angle’. Arcs ‘crossing the line at 90°’ is evidence of an inappropriate method.] AND Intersecting arcs (equal radii) using the above two points as centres. Ignore line extended above XY for M1.
Line drawn
A1
Ignore line extended above XY for M1A1.
Alternative method
Scheme
Marks
Comments
(Using the properties of a kite.) All correct construction arcs shown.
M1
Intersecting arcs whose centres are any two points on the line XY and respective radii equal in length to the distance from the points to the point P.
[Note to markers: The arcs will always intersect at a point that is a ‘reflection of point P’ in the line XY.]
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