Answer:
Translation: Shift the trapezoid 5 units to the right.
Dilation: Enlarge the trapezoid vertically by a factor of approximately 3.365.
Reflection: Reflect the trapezoid across the y-axis.
Note: The order of transformations may vary depending on the convention used.
Explanation:
To determine the series of transformations that result in the unshaded trapezoid being the image of the shaded trapezoid, we can analyze the changes in the coordinates.
Translation:
The shaded trapezoid is shifted horizontally by 5 units to the right to become the unshaded trapezoid. Therefore, the first transformation is a translation.
Translation vector = (5, 0)
Dilation:
The shaded trapezoid is enlarged in the vertical direction. To determine the dilation factor, we compare the corresponding side lengths.
The length of side AB in the shaded trapezoid is given by the distance formula:
AB = sqrt((-4 - (-5))^2 + (5 - 1)^2) = sqrt(1^2 + 4^2) = sqrt(17)
The length of side A'B' in the unshaded trapezoid is given by the distance formula as well:
A'B' = sqrt((1.5 - 0)^2 + (9 - 1)^2) = sqrt(1.5^2 + 8^2) = sqrt(66.25) = 2.5sqrt(26)
The dilation factor is the ratio of the corresponding side lengths:
Dilation factor = A'B' / AB = (2.5sqrt(26)) / sqrt(17) = 2.5sqrt(26/17) ≈ 3.365
Reflection:
The unshaded trapezoid is a reflection of the shaded trapezoid across the y-axis. This transformation reverses the sign of the x-coordinates.