To find the scale factor used to dilate the quadrilateral, we can compare the corresponding vertices of the original quadrilateral and the dilated quadrilateral.
Let’s denote the original vertices as follows:
- \( A(4, 4) \)
- \( B(6, 6) \)
- \( C(8, 4) \)
- \( D(6, 2) \)
And the new, dilated vertices as:
- \( A'(3, 3) \)
- \( B'(4.5, 4.5) \)
- \( C'(6, 3) \)
- \( D'(4.5, 1.5) \)
We will use the formula for scale factor \( k \):
\[ k = \frac{\text{New Coordinate}}{\text{Original Coordinate}} \]
Now we can compute the scale factor for each corresponding vertex:
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For point \( A(4, 4) \) to \( A'(3, 3) \): \[ k_A = \frac{3}{4} = 0.75 \]
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For point \( B(6, 6) \) to \( B'(4.5, 4.5) \): \[ k_B = \frac{4.5}{6} = 0.75 \]
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For point \( C(8, 4) \) to \( C'(6, 3) \): \[ k_C = \frac{6}{8} = 0.75 \]
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For point \( D(6, 2) \) to \( D'(4.5, 1.5) \): \[ k_D = \frac{4.5}{6} = 0.75 \]
Since all calculated scale factors are equal to \( 0.75 \), the scale factor used to dilate the quadrilateral is
\[ \boxed{0.75} \]