The quadrilateral A'B'C'D' is the result of reflecting and translating the quadrilateral ABCD.
<h3>What kind of rigid transformations were done to transform ABCD to A'B'C'D'?</h3>
In this problem we find a representation of a quadrilateral and its image on a Cartesian plane. That image is the result of the following rigid transformations, that is, transformations applied on geometric loci such that Euclidean distance is conserved at every point of the locus.
After a careful inspection, we find that the following two rigid transformations were done:
- Reflection about the x-axis.
- Translation 7 units in the + x direction.
Now let is prove this steps:
Given: A(x, y) = (- 5, - 7), B(x, y) = (- 5, - 2), C(x, y) = (- 3, - 4), D(x, y) = (- 3, - 7)
Reflection:
A''(x, y) = (- 5, - 7) + (0, 14)
A''(x, y) = (- 5, 7)
B''(x, y) = (- 5, - 2) + (0, 4)
B''(x, y) = (- 5, 2)
C''(x, y) = (- 3, - 4) + (0, 8)
C''(x, y) = (- 3, 4)
D''(x, y) = (- 3, - 7) + (0, 14)
D''(x, y) = (- 3, 7)
Translation
A'(x, y) = (- 5, 7) + (7, 0)
A'(x, y) = (2, 7)
B'(x, y) = (- 5, 2) + (7, 0)
B'(x, y) = (2, 2)
C'(x, y) = (- 3, 4) + (7, 0)
C'(x, y) = (4, 4)
D'(x, y) = (- 3, 7) + (7, 0)
D'(x, y) = (4, 7)
To learn more on rigid transformations: brainly.com/question/1761538
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