Let's use the dilation formula to find the image of each vertex after dilation.
The dilation formula is:
(x', y') = (k * x, k * y)
For each vertex, the scale factor k = 2/3, because the coordinates after dilation are 2/3 of the original coordinates.
Vertex 1: (4, 4)
x' = (2/3) * 4 = 8/3
y' = (2/3) * 4 = 8/3
New vertex 1: (8/3, 8/3) or (2.67, 2.67)
Vertex 2: (6, 6)
x' = (2/3) * 6 = 4
y' = (2/3) * 6 = 4
New vertex 2: (4, 4)
Vertex 3: (8, 4)
x' = (2/3) * 8 = 16/3
y' = (2/3) * 4 = 8/3
New vertex 3: (16/3, 8/3) or (5.33, 2.67)
Vertex 4: (6, 2)
x' = (2/3) * 6 = 4
y' = (2/3) * 2 = 4/3
New vertex 4: (4, 4/3) or (4, 1.33)
Therefore, the new quadrilateral has the following vertices after dilation:
(8/3, 8/3), (4, 4), (16/3, 8/3), (4, 4/3) or (2.67, 2.67), (4, 4), (5.33, 2.67), (4, 1.33).
a quadrilateral has the following vertices: (4,4), (6,6), (8,4), (6,2). after dilation, the new quadrilateral has the following vertices: (3,3), (4,5, 4,5), (6,3), (4,5, 1,5)
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