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12.2 Solving transformation problems

Worked example 12.2b

The diagram shows shape A on a coordinate grid. y
One corner of shape A is marked with a red cross. 6
Harsha rotated shape A 90° clockwise about the point (4, 1) and labelled 5
the image shape B. 4
She refl ected shape A in the line x = 4 and labelled the image shape C. 3
A
2
The red crosses on shapes B and C
1
have exactly the same coordinates.
0 x
0 1 2 3 4 5 6 7
a Show that what Harsha said is correct.
b Write down the coordinates of the red cross on shapes B and C.

a x = 4 First, rotate shape A through 90° clockwise about the point (4, 1).
y The easiest way to do this is to use tracing paper. Carefully trace shape
6 A, then put the point of the pencil on the point (4, 1). Turn the tracing
5 paper 90° clockwise, then draw the image of shape A.
4 Label this image shape B.
B
3 Draw the line x = 4 onto the grid and refl ect shape A in the line.
A
2 Draw the image and label it shape C.
C It is clear that the red cross on shapes B and C have exactly the same
1
0 x coordinates.
0 1 2 3 4 5 6 7
b The coordinates of the red cross on shapes B and C are (5, 2).

) Exercise 12.2

1 The diagram shows shape A on a coordinate grid. 3 y
Copy the grid, then draw the image of shape A after each translation. 2
3  
a   b   4  c  −  2   d  −  1  1


2   −  2  2  −  2  –4 –3 –2 A –1 0 1 2 3 4 x
–1
–2
–3

2 The diagram shows triangle B on a coordinate grid. y
Make two copies of the grid. 6

a On the first copy, draw the image of triangle B after reflection 5 4
in the line:
i x = 4 ii y = 3 iii x = 4.5 iv y = 4 3 2
b On the second copy, draw the image of triangle B after a rotation: 1 B
i 90° clockwise about the point (4, 1) 0
ii 90° anticlockwise about the point (1, 1) 0 1 2 3 4 5 6 7 x
iii 180° about the point (2, 4)
iv 180° about the point (4, 3)

114 12 Tessellations, transformations and loci