Question

is quadrilateral jklm the result of a dilation of quadrilateral abcd by a scale factor of 2? why or why not?
yes, because sides jk and ml are twice as long as sides ab 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 ab and dc.
no, because sides jm and kl have different slopes from sides ad and bc

Explanation:

Step1: Understand dilation

Dilation is a transformation that changes the size of a figure but not its shape. Corresponding sides of dilated figures are proportional and corresponding sides are parallel (same slope).

Step2: Analyze the slopes

• For a dilation with scale factor \(2\), all corresponding sides should be parallel (same slope).
• Calculate the slopes of \(AD\) and \(JM\), \(BC\) and \(KL\). If slopes are different, it's not a dilation.
• Since sides \(JM\) and \(KL\) have different slopes from sides \(AD\) and \(BC\), quadrilateral \(JKLM\) is not the result of a dilation of quadrilateral \(ABCD\) by a scale factor of \(2\).

Answer:

No, because sides JM and KL have different slopes from sides AD and BC