To determine the nature of the transformation between the two trapezoids given their side lengths, let's analyze the side lengths and the properties of the trapezoids.
Trapezoid 1 has side lengths: 4, 2, 6, 2. Trapezoid 2 has side lengths: 8, 4, 12, 4.
Next, we can analyze the relationships between the corresponding side lengths of both trapezoids:
-
The longer side of Trapezoid 1 (length 6) corresponds to the longer side of Trapezoid 2 (length 12). The ratio of these lengths is: \[ \frac{12}{6} = 2. \]
-
The shorter parallel side of Trapezoid 1 (length 4) corresponds to the shorter parallel side of Trapezoid 2 (length 8). The ratio here is: \[ \frac{8}{4} = 2. \]
-
The non-parallel sides of Trapezoid 1 (both 2) correspond to the non-parallel sides of Trapezoid 2 (both 4). The ratio is: \[ \frac{4}{2} = 2. \]
Since all corresponding side lengths have the same ratio (2), we can conclude that the transformation from Trapezoid 1 to Trapezoid 2 is a dilation, where the trapezoids are similar (the angle measures being identical confirms similarity).
Now, we also need to evaluate whether the transformation is isometric. A transformation is isometric if it preserves distances. Since the sizes of the trapezoids have changed (Trapezoid 2 is larger than Trapezoid 1), this transformation is not isometric.
Therefore, the correct description of the transformation is:
It is a dilation because the transformation is not isometric.
3 answers