9.4 CHAPTER 9. GEOMETRY
Description
Transformation (translation, reflection, Co-ordinates Lengths Angles
rotation, enlargement)
A�(2;−6) A�B�= 3 Bˆ�= 90◦
(x;y)→ (x;−y) reflection about the x-axis B�(5;−6) B�C�= 4 tanAˆ = 4/ 3
C�(5;−2) A�C�= 5 ∴Aˆ = 53◦,Cˆ = 37◦(x;y)→ (x + 1;y− 2)(x;y)→ (−x;y)(x;y)→ (−y;x)(x;y)→ (−x;−y)(x;y)→ (2x; 2y)(x;y)→ (y;x)(x;y)→ (y;x + 1)A transformation that leaves lengths and angles unchanged is called a rigid transformation.
Which of the above transformations are rigid?Chapter 9 End of Chapter Exercises
- ΔABC undergoes several transformations forming ΔA�B�C�. Describe the relation-
ship between the anglesand sides of ΔABC and ΔA�B�C�(e.g., they are twice as
large, the same, etc.)
Transformation Sides Angles Area
Reflect
Reduce by a scale factorof 3
Rotate by 90 ◦
Translate 4 units right
Enlarge by a scale factorof 2 - ΔDEF hasEˆ = 30◦, DE = 4 cm, EF = 5 cm. ΔDEF is enlarged by a scale factor
of 6 to form ΔD�E�F�.
(a) Solve ΔDEF
(b) Hence, solve ΔD�E�F� - ΔXYZ has an area of 6 cm^2. Find the area of ΔX�Y�Z�if the points have been
transformed as follows:
(a) (x,y)→ (x + 2;y + 3)
(b) (x,y)→ (y;x)