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1. The points that represent the translations of the point A(x, y) = (1, – 2) are A'(x, y) = (- 4, – 1) and A”(x, y) = (- 1, – 1). (Correct choice: 4)

   What is the resulting point by applying translations?

   Rigid transforations are transformations applied on geometric loci such that Herein we know the coordinates of a point on a Cartesian plane, on which two translation vectors, a kind of rigid transformation, are applied to determine the coordinates of the resulting point according to the following formula:

   P'(x, y) = P(x, y) + T₁(x, y)       (1)

   P”(x, y) = P'(x, y) + T₂(x, y)     (2)

   Where:

   • P(x, y) – Original point
   • P'(x, y), P”(x, y) – Resulting points.
   • T₁(x, y), T₂(x, y) – Translation vectors.

   If we know that A(x, y) = (1, – 2), T₁(x, y) = (- 5, 1) and T₂(x, y) = (3, 0), then the resulting points are:

   A'(x, y) = (1, – 2) + (- 5, 1)

   A'(x, y) = (- 4, – 1)

   A”(x, y) = (- 4, – 1) + (3, 0)

   A”(x, y) = (- 1, – 1)

   Then, the points that represent the translations of the point A(x, y) = (1, – 2) are A'(x, y) = (- 4, – 1) and A”(x, y) = (- 1, – 1). (Correct choice: 4)

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

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