Is quadrilateral JKLM the result of a dilation of quadrilateral ABCD by a scale factor of 2 ? Why or why not? Yes, betause sides JK and ML are twice as long as sides \( A B \) and DC. Yes, because both figures are parallelograms, so corresponding sides are parallel. No, because sides JK and ML are not twice as long as sides \( A B \) and DC. No, because sides JM and KL have different slopes from sides \( A D \) and \( B C \)

To determine if quadrilateral JKLM is the result of a dilation of quadrilateral ABCD by a scale factor of 2, we need to consider several factors: 1. **Scale Factor**: The scale factor of 2 means that each side of quadrilateral JKLM should be twice as long as the corresponding side of quadrilateral ABCD. 2. **Parallel Sides**: While it's true that both figures are parallelograms, this alone does not confirm that JKLM is a dilation of ABCD. Parallel sides in both figures do not provide enough information to determine the scale factor. 3. **Slope of Sides**: The slopes of the sides are not relevant to determining if one figure is a dilation of another. Dilation is a transformation that changes the size of a figure, not its orientation or slope. Let's analyze the given statements: - **Statement 1**: "Yes, because sides JK and ML are twice as long as sides AB and DC." - This statement is correct. If sides JK and ML are indeed twice as long as sides AB and DC, then this supports the idea that JKLM is a dilation of ABCD by a scale factor of 2. - **Statement 2**: "Yes, because both figures are parallelograms, so corresponding sides are parallel." - This statement is not sufficient to conclude that JKLM is a dilation of ABCD. Parallel sides alone do not confirm the scale factor. - **Statement 3**: "No, because sides JK and ML are not twice as long as sides AB and DC." - This statement is incorrect if sides JK and ML are indeed twice as long as sides AB and DC. - **Statement 4**: "No, because sides JM and KL have different slopes from sides AD and BC." - This statement is irrelevant to the question of whether JKLM is a dilation of ABCD. Based on the analysis, the correct answer is: **Yes, because sides JK and ML are twice as long as sides AB and DC.** This statement directly addresses the scale factor of 2, which is the defining characteristic of a dilation.