Date | November 2020 | Marks available | 2 | Reference code | 20N.1.AHL.TZ0.F_7 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 0 |
Command term | Find | Question number | F_7 | Adapted from | N/A |
Question
Points in the plane are subjected to a transformation T in which the point (x, y) is transformed to the point (x', y') where
[x'y']=[3002][xy].
Describe, in words, the effect of the transformation T.
Show that the points A(1, 4), B(4, 8), C(8, 5), D(5, 1) form a square.
Determine the area of this square.
Find the coordinates of A', B', C', D', the points to which A, B, C, D are transformed under T.
Show that A' B' C' D' is a parallelogram.
Determine the area of this parallelogram.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
a stretch of scale factor 3 in the x direction
and a stretch of scale factor 2 in the direction A1
[1 mark]
the four sides are equal in length A1
A1
so product of gradients , therefore is perpendicular to A1
therefore is a square AG
[3 marks]
area of square A1
[1 mark]
the transformed points are
A2
Note: Award A1 if one point is incorrect.
[2 marks]
A1
therefore is parallel to R1
A1
therefore is parallel to
therefore is a parallelogram AG
[3 marks]
(M1)
A1
[2 marks]