Transformations in Geometry

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In a 2-dimensional coordinate plane, a given object can be transformed by changing its position, its inclination or its size.  There are 4 important types of transformations commonly used in geometry. They are: translation, rotation, reflection and dilation. These 4 types of transformations change the object as it slides turns, flips or the size changes respectively. During translation, rotation and reflection the size of the object never changes, however during dilation the size of the object either enlarges or shrinks.
 
Example 1: The length of a side of an object is 12 units. The length of the image of the same object is 3units. Which transformation is used here?

Given: object side length = 12 units

Image side length = 3 units.

Here, clearly the size of the object has been changed since the length of the object is changed.

Therefore the transformation used here is Dilation.

Scale factor = (Image length) / (Object length) = 3/12 = 1/4

This implies that the object’s size has been reduced by a scale factor of 1/4!
 
Example 2: In an X-Y coordinate plane, PQR is a triangle where point P is at (3, 2). The image of the triangle P’Q’R’ has the point P’ at (0, 6). Which transformation is used here?

Given: point P= (3, 2) and point P’= (0, 6)

Since the points have been moved, hence the transformation used here is Translation!

The ‘x’ coordinate has changed from 3 to 0==>change= 0– (3) = -3 = 3 units to the left.

The ‘y’ coordinate has changed from 2 to 6 ==> change= 6– (2) = 4 units up.

 

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