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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).

[2]
a.

Given that T:(pq)2(pq), find the value of p and the value of q.

[3]
b.

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.

[2]
c.

Markscheme

(7 -102 -3)(6-2)+(-54)             (M1)

=(5722)  OR  (57, 22)            A1


[2 marks]

a.

(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]

b.

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]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 3—Geometry and trigonometry » AHL 3.9—Matrix transformations
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Topic 3—Geometry and trigonometry

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