Quadrilateral ABCD is graphed on a coordinate grid with vertices at A (─2, 0), B (─-1, 3), C (3, 4), and D (4, ─3). Quadrilateral ABCD is dilated by a scale factor of u with the origin as the center of dilation to create quadrilateral A’B’C’D’. What is the ordered pair that would represent the coordinates of vertex D’?
To find the coordinates of vertex D' after the dilation, we need to use the formula for dilation:
D'(x, y) = u * (D - O) + O
Where D(x, y) are the coordinates of vertex D, O(0, 0) is the center of dilation, and u is the scale factor.
Given that the scale factor is u, which means the dilation is centered at the origin, we can find the new coordinates of D' by multiplying the coordinates of D by the scale factor u.
D' = u * D
D'(x, y) = u(4, -3)
D'(x, y) = (4u, -3u)
Therefore, the coordinates of vertex D' after the dilation would be (4u, -3u).