By applying the concept of translation, we conclude that the <em>image</em> point of (1, - 2) is equal to the point (5, - 6).
<h3>What is the image of a point by rigid translations?</h3>
In this problem we have a point set in a <em>Cartesian</em> plane, which has to be translated to determine the coordinates of a <em>resulting</em> point. Translations are examples of <em>rigid</em> transformations, these are, transformations applied on <em>geometric</em> loci such that <em>Euclidean</em> distance is conserved.
Vectorially speaking, translations are modelled by the following formula:
P'(x, y) = P(x, y) + T(x, y) (1)
Where:
- P(x, y) - Original point
- P'(x, y) - Resulting point
- T(x, y) - Translation vector
If we know that P(x, y) = (1, - 2) and T(x, y) = (4, - 4), then the resulting point is:
P'(x, y) = (1, - 2) + (4, - 4)
P'(x, y) = (5, - 6)
By applying the concept of translation, we conclude that the <em>image</em> point of (1, - 2) is equal to the point (5, - 6).
To learn more on rigid transformations: brainly.com/question/1761538
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