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Quadrilateral ABCD has vertices at A (0, 0), B (0, 3), C (5, 3), and D (5, 0). Find the vertices of the
quadrilateral after a dilation with scale factor 2.5.

Sagot :

xero099

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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