According to the dilation formula, the location of the four vertices of the quadrilateral A'B'C'D' are A'(x, y) = (0, 0), B'(x, y) = (0, 7.5), C'(x, y) = (12.5, 7.5) and D'(x, y) = (12.5, 0).
How to determine the coordinates of the vertices of the dilated rectangle
Dilation are a kind of rigid transformations defined by the following formula:
P'(x, y) = O(x, y) + r · [P(x, y) - O(x, y)] (1)
Where:
- O(x, y) - Center of dilation
- r - Dilation factor
- P(x, y) - Original point
- P'(x, y) - Resulting point
If we know that r = 2.5, O(x, y) = (0, 0), A(x, y) = (0, 0), B(x, y) = (0, 3), C(x, y) = (5, 3) and D(x, y) = (5, 0), then the resulting points are obtained:
A'(x, y) = (0, 0) + 2.5 · [(0, 0) - (0, 0)]
A'(x, y) = (0, 0)
B'(x, y) = (0, 0) + 2.5 · [(0, 3) - (0, 0)]
B'(x, y) = (0, 7.5)
C'(x, y) = (0, 0) + 2.5 · [(5, 3) - (0, 0)]
C'(x, y) = (12.5, 7.5)
D'(x, y) = (0, 0) + 2.5 · [(5, 0) - (0, 0)]
D'(x, y) = (12.5, 0)
Lastly, we proceed to graph the two figures.
To learn more on dilations: https://brainly.com/question/13176891
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