After dilating the quadrilateral ABCD by a factor of 2 and with respect to the origin, the point A(x, y) = (-3, -1) is transformed into the point A'(x, y) = (-9, -3).
<h3>How to determine the coordinates of an image after applying a rigid transformation</h3>
First of all, dilation is a type of <em>rigid</em> transformation. <em>Rigid</em> transformations are transformations applied on <em>geometric</em> loci such that the <em>Euclidean</em> distance at every point of the construction is conserved. Vectorially speaking, the dilation is expressed by the following formula:
A'(x, y) = A(x, y) + k · [A(x, y) - O(x, y)] (1)
Where:
- A(x, y) - Original point
- O(x, y) - Center of dilation
- A'(x, y) - Resulting point
- k - Dilation factor
If we know that A(x, y) = (-3, -1), k = 2 and O(x, y) = (0, 0), then the coordinates of A' are:
A'(x, y) = (-3, -1) + 2 · [(-3, -1) - (0, 0)]
A'(x, y) = (-3, -1) + (-6, -2)
A'(x, y) = (-9, -3)
After dilating the quadrilateral ABCD by a factor of 2 and with respect to the origin, the point A(x, y) = (-3, -1) is transformed into the point A'(x, y) = (-9, -3).
To learn more on dilations: brainly.com/question/13176891
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