| 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 y direction A1
[1 mark]
the four sides are equal in length (5) A1
Grad AB=43, Grad BC=-34 A1
so product of gradients =-1, therefore AB is perpendicular to BC A1
therefore ABCD is a square AG
[3 marks]
area of square =25 A1
[1 mark]
the transformed points are
A'=(3, 8)
B'=(12,16)
C'=(24,10)
D'=(15, 2) A2
Note: Award A1 if one point is incorrect.
[2 marks]
Grad A'B'=89; Grad C'D'=89 A1
therefore A'B' is parallel to C'D' R1
Grad A'D'=-612; Grad B'C'=-612 A1
therefore A'D' is parallel to B'C'
therefore A' B' C' D' is a parallelogram AG
[3 marks]
area of parallelogram=|determinant|×area of square
=6×25 (M1)
=150 A1
[2 marks]
