Transformation Math

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Transformations in math refer to the ways in which a given geometric shape can be transformed in the coordinate plane by the methods of reflection, rotation, translation or dilation. The process of reflection, rotation and translation mean that the given shape is being flipped, turned or moved respectively in a certain direction in the coordinate plane. However, with these three methods the object’s size never changes and stays the same. But Dilation is a method in which the object’s size is changed by a certain scale factor.
 
Example 1: In an X-Y coordinate plane, ABCD is rectangle where point A is at (1, 4). The image of the rectangle A’B’C’D’ has the point A’ at (-3, -1). Which transformation is used here?

Given: point A= (1, 4) and point A’= (-3, -1)

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

The ‘x’ coordinate has changed from 1 to -3 =>change= 1– (-3) = 4 units to the left.

The ‘y’ coordinate has changed from 4 to -1==> change= 4– (-1) = 5 units down.
 
 Example 2: The length of a side of an object is 6 units. The length of the image of the same object is 18units. Which transformation is used here?

Given: object side length = 6 units

Image side length = 18 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) = 18/6 = 3

This implies that the object has been enlarged by a scale factor of 3!
 


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