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

(\begin{array}{l} a \\ b \end{array}),

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

(\begin{array}{l} 4 \\ - 3 \end{array})

and B (1, –2) under a translation

(\begin{array}{l} - 5 \\ 3 \end{array})

Solution:

A’ = [–2 + 4, 4 + (–3)] = (2, 1)

B’ = [1 + (–5), –2 + 3] = (–4, 1)

Example 2:

Point K moved to point K’ (3, 8) under a translation

(\begin{array}{l} - 4 \\ 3 \end{array}) .

What are the coordinates of point K?

Solution:

K (x, y) \to (\begin{array}{l} - 4 \\ 3 \end{array}) \to 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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