Question

Which of the following represents the translation of R (-3, 4) along the vector

Answer 1

By applying concepts of linear algebra, the point P'(x, y) = (-3, 4) represents the translation of P(x, y) = (-3, 4) along the vectors <7, -6> and <-1, 3>.

How to determine the resulting point by applying translations

Translations are a kind of rigid transformation. A transformation is rigid if and only if Euclidean distances are conserved. By linear algebra, an image as a consequence of consecutive translations is described by the following formula:

$P' (x,y) = P(x,y) + \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)$     (1)

Where:

• P(x, y) - Original point
• P'(x, y) - Image
• $\left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)$ - Net translation vector

Now we proceed to determine the image of the given point:

P'(x, y) = (-3, 4) + (7, -6) + (-1, 3)

P'(x, y) = (-3 + 7 - 1, 4 - 6 + 3)

P'(x, y) = (3, 1)

By applying concepts of linear algebra, the point P'(x, y) = (-3, 4) represents the translation of P(x, y) = (-3, 4) along the vectors <7, -6> and <-1, 3>.

To learn more on rigid transformations: brainly.com/question/1761538

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