Intermediate November 2017 Unit 1 Q12
12. Using only a ruler and a pair of compasses, construct a perpendicular line from the point \(P\) to the line \(AB\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| Arc, centre P, intersecting AB at two points. (B may be one of the points with no arc seen at point B) | M1 | [Note to markers: These arcs may be identified by the fact that they will ‘cross the line AB at an acute angle’. Arcs ‘crossing the line at 90°’ is evidence of an inappropriate method.] |
| Intersecting arcs (equal radii) using the above two points as centres. | m1 | |
| Line drawn | A1 | M1 and m1 must be gained before A1 is awarded. |
Alternative method.
Using the properties of a kite.
| Scheme | Marks | Comments |
|---|---|---|
| Intersecting arcs whose centres are any two points on the line AB and respective radii equal in length to the distance from the points to the point P. | M2 | [Note to markers: The arcs will always intersect at a point that is a ‘reflection of point P’ in the line AB.] |
| Line drawn | A1 |