Cambridge International Mathematics

Transformation geometry (Chapter 20) 405

Example 3 Self Tutor

Find the image of the point(3,1)under a rotation about O(0,0)which is:

a 90 oanticlockwise b 90 oclockwise c 180 o:

a (3,1)! (¡ 1 ,3)

b (3,1)! (1,¡3)

c (3,1)! (¡ 3 ,¡1)

Example 4 Self Tutor

Triangle ABC has vertices A(¡ 1 ,2),B(¡ 1 ,5) and C(¡ 3 ,5). It is rotated

clockwise through 90 oabout(¡ 2 ,0). Draw the image of triangle ABC and

label it A^0 B^0 C^0.

A(¡ 1 ,2) !A^0 (0,¡1)

B(¡ 1 ,5)! B^0 (3,¡1)

C(¡ 3 ,5)! C^0 (3,1)

Example 5 Self Tutor

Find the image equation of the line 2 x¡ 3 y=¡ 6 under a clockwise rotation about O(0,0)

through 90 o.

2 x¡ 3 y=¡ 6

hasx-intercept¡ 3 (when y=0)

andy-intercept 2 (when x=0)

We hence graph 2 x¡ 3 y=¡ 6 fdashedg

Next we rotate these intercepts clockwise through 90 o.

The image hasx-intercept 2 andy-intercept 3.

The gradient of the image is m=¡^32 and the

y-intercept c=3.

) the image equation is y=¡^32 x+3.

y

x

(3'\\1)

(1'-3)

(-1'\\3)

(-3'\-1)

O

DEMO

y

O x

-4 -2 2 4

-2

2

4

6

centre

()-2 ¡0,

CB

A

A' B'

C'

y

x

-3 2

2

3

2!-3@=-6

y=- 23 x+ 3

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Y:\HAESE\IGCSE01\IG01_20\405IGCSE01_20.CDR Thursday, 16 October 2008 2:55:13 PM PETER