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).
How to determine the coordinates of an image after applying a rigid transformation
First of all, dilation is a type of rigid transformation. Rigid transformations are transformations applied on geometric loci such that the Euclidean 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: https://brainly.com/question/13176891
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