Question

is quadrilateral j k l m the result of a dilation of quadrilateral a b c d by a scale factor of 2? why or why not?
yes, because sides j k and m l are twice as long as sides a b and d c.
yes, because both figures are parallelograms, so corresponding sides are parallel.
no, because sides j k and m l are not twice as long as sides a b and d c.
no, because sides j m and k l have different slopes from sides a d and b c.

Explanation:

Step1: Understand the concept of dilation

Dilation is a transformation that enlarges or reduces a figure by a scale factor. All corresponding sides of the dilated figure and the original figure should be in proportion to the scale factor.

Step2: Analyze each option

• Option 1: Just checking two sides (JK and ML) is not sufficient. For dilation, all corresponding sides should have the same scale - factor relationship.
• Option 2: Both being parallelograms (having parallel sides) is a property of the shape but not the criterion for dilation. Dilation is about size (side - length proportion) and similarity (not just shape type).
• Option 3: If it were a dilation with scale factor 2, all corresponding sides should be twice as long. Since sides JK and ML (and other corresponding sides) are not twice as long as sides AB and DC (by visual inspection of the grid - based lengths), this option is correct.
• Option 4: Slope is related to the orientation of the sides. Dilation is about size (side - length proportion), not the slope of the sides.

Answer:

No, because sides JK and ML are not twice as long as sides AB and DC.