11.1.1 Isometric Transformations


11.1 Isometric Transformations

11.1.1 Transformation
A transformation is a one-to-one correspondence or mapping between points of an object and its image on a plane. 


11.1.2 Translation
1. A translation is a transformation which moves all the points on a plane through the same distance in the same direction.
 
2. Under a translation, the shape, size and orientation of object and its image are the same.
 
3. A translation in a Cartesian plane can be represented in the form ( a b ) ,  whereby, a represents the movement to the right or left which is parallel to the x-axis and b represents the movement upwards or downwards which is parallel to the y-axis.


Example 1:
Write the coordinates of the image of A (–2, 4) under a translation ( 4 3 )  and B (1, –2) under a translation ( 5 3 ) .

Solution
:

 
A’ = [–2 + 4, 4 + (–3)] = (2, 1)
B’ = [1 + (–5), –2 + 3] = (–4, 1)

Example 2
:
Point moved to point K’ (3, 8) under a translation ( 4 3 ) .  
What are the coordinates of point K?

Solution
:
K ( x , y ) ( 4 3 ) K ' ( 3 , 8 )
The coordinates of K = [3 – (– 4), 8 – 3]
= (7, 5)

Therefore the coordinates of K are (7, 5).


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