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How many distinct linear functions mapping the square D onto the square E are there?

In Example 4.1, we have found one so far.

Example 4.1: Find the linear function which maps the square D with side 2 onto the square E with side 4 (Fig. 26) and maps point A to point B.

Answer :

Final answer:

In the context of Mathematics, looking at an affine mapping in a two-dimensional plane, there is only one distinct linear function that maps square D with side 2 onto square E with side 4, while also mapping point A to point B.

Explanation:

In the field of Mathematics, the number of distinct linear functions that map one square onto another depends primarily on the number of fixed points. In Example 4.1, a linear function was found that mapped square D onto square E while also mapping point A to point B, denoting two fixed points. In a general setting, for an affine mapping (or linear transformation) in a 2-dimensional plane, which is our case considering we are dealing with squares, there is only one unique linear function for two fixed points.

Therefore, taking into consideration the two fixed points, we can conclude that there is only one distinct linear function that maps square D onto square E.

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