Date | May 2021 | Marks available | 2 | Reference code | 21M.1.AHL.TZ2.14 |
Level | Additional Higher Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Explain | Question number | 14 | Adapted from | N/A |
Question
A geometric transformation T:(xy)↦(x'y') is defined by
T:(x'y')=(7 -102 -3)(xy)+(-54).
Find the coordinates of the image of the point (6, −2).
Given that T:(pq)↦2(pq), find the value of p and the value of q.
A triangle L with vertices lying on the xy plane is transformed by T.
Explain why both L and its image will have exactly the same area.
Markscheme
(7 -102 -3)(6-2)+(-54) (M1)
=(5722) OR (57, 22) A1
[2 marks]
(2p2q)=(7 -102 -3)(pq)+(-54) (M1)
7p-10q-5=2p
2p-3q+4=2q (A1)
solve simultaneously:
p=13, q=6 A1
Note: Award A0 if 13 and 6 are not labelled or are labelled the other way around.
[3 marks]
det(7 -102 -3)=-1 (OR |det (7 -102 -3)|=1) A1
scale factor of image area is therefore (|-1|=)1 (and the translation does not affect the area) A1
[2 marks]