Higher November 2019 Unit 1 Q5
5.
(a) Using only a ruler and a pair of compasses, construct a triangle \(PQR\), so that it satisfies both of the following conditions:
- \(P\widehat{Q}R = 60^\circ\),
- \(PQ = 7\,\text{cm}\).
(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]
| Scheme | Marks | Comments |
|---|---|---|
| Correct construction of 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. |
| 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.] |
| Line drawn. | A1 |