Cambridge International Mathematics

Transformation geometry (Chapter 20) 411

Example 9 Self Tutor

Consider the triangle ABC with A(1,1),B(5,1)and C(1,4)under a stretch

with invariantx-axis and scale factor: a k=2 b k=^12.

Find the position of the image of¢ABC under each stretch.

ab

STRETCHES WITH INVARIANTy-AXIS

Suppose P(x,y)moves to P^0 (x^0 ,y^0 )such that P^0 lies on the line

through N(0,y)and P, and NP^0 =kNP.

Example 10 Self Tutor

Consider the triangle ABC with A(1,1),B(5,1)and C(1,4)under a stretch

with invarianty-axis and scale factor: a k=2 b k=^12.

Find the position of the image of¢ABC under each stretch.

ab

y

x

N

P(!' @) P' ' '(! ' @ )

y

x

k=2

A

A'

C

C'

B

B'

5

O 5

y

x

k=Qw_

A

A'

C

C'

B

B'

5

O 5

y

x

k¡=¡2

A A'

CC'

B B'

5

O 5

y

x

k¡=¡¡Qw_

A'A

C'C

B' B

5

O 5

For a stretch with invarianty-axis and scale factork,

(x,y)!(kx,y).

We call this astretch with invariant -axisy and scale factor .k

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Y:\HAESE\IGCSE01\IG01_20\411IGCSE01_20.CDR Thursday, 16 October 2008 2:55:47 PM PETER