The second figure is the result of two reflections (x-axis, y-axis) and a dilation (factor: 0.5) with respect to the origin of the first figure. (Correct choice: A)
How to transform a geometric locus by rigid transformations
In this question we have a geometric locus whose vertices are A(x, y) = (2, 1), B(x, y) = (3, 1), C(x, y) = (3, 3), D(x, y) = (4, 5), E(x, y) = (1, 5), F(x, y) = (2, 3), which can be modified by applying a sequence of rigid transformations, defined as transformations that modify geometric loci without altering Euclidean distance.
We proceed to apply the following sequence:
(i) Reflection across the x-axis: P'(x, y) = (x, - y).
A'(x, y) = (2, - 1), B'(x, y) = (3, - 1), C'(x, y) = (3, - 3), D'(x, y) = (4, - 5), E'(x, y) = (1, - 5), F'(x, y) = (2, - 3)
(ii) Reflection across the y-axis: P''(x, y) = (- x, y).
A''(x, y) = (- 2, - 1), B''(x, y) = (- 3, - 1), C''(x, y) = (- 3, - 3), D''(x, y) = (- 4, - 5), E''(x, y) = (- 1, - 5), F''(x, y) = (- 2, - 3)
(iii) Dilation with respect to the origin by a factor of 0.5: P'''(x, y) = 0.5 · (x, y)
A'''(x, y) = (- 1, - 0.5), B'''(x, y) = (- 1.5, - 0.5), C'''(x, y) = (- 1.5, - 1.5), D'''(x, y) = (- 2, - 2.5), E'''(x, y) = (- 0.5, - 2.5), F'''(x, y) = (- 1, - 1.5).
Therefore, the second figure is the result of two reflections (x-axis, y-axis) and a dilation (factor: 0.5) with respect to the origin of the first figure. (Correct choice: A)
To learn more on rigid transformations: https://brainly.com/question/28004150
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