is quadrilateral jklm the result of a dilation of quadrilateral abcd by a scale factor of 2? why or why…

is quadrilateral jklm the result of a dilation of quadrilateral abcd by a scale factor of 2? why or why not?\nyes, because sides jk and ml are twice as long as sides ab and dc.\nyes, because both figures are parallelograms, so corresponding sides are parallel.\nno, because sides jk and ml are not twice as long as sides ab and dc.\nno, because sides jm and kl have different slopes from sides ad and bc.

is quadrilateral jklm the result of a dilation of quadrilateral abcd by a scale factor of 2? why or why not?\nyes, because sides jk and ml are twice as long as sides ab and dc.\nyes, because both figures are parallelograms, so corresponding sides are parallel.\nno, because sides jk and ml are not twice as long as sides ab and dc.\nno, because sides jm and kl have different slopes from sides ad and bc.

Answer

Explanation:

Step1: Recall dilation property

In a dilation by scale - factor (k), all corresponding side - lengths are multiplied by (k). Here (k = 2).

Step2: Analyze side - lengths

We need to check if all corresponding sides of quadrilateral (JKLM) are twice as long as the corresponding sides of quadrilateral (ABCD). Just checking two pairs of sides ((JK) and (AB), (ML) and (DC)) is not enough. We need to check all pairs of corresponding sides. In a dilation, the ratio of corresponding side - lengths should be the same for all sides.

Step3: Evaluate the options

Option A only checks two pairs of sides. Option B is wrong because being a parallelogram does not imply a dilation relationship. Option D about slopes is not relevant to the property of dilation (dilation is about side - length ratio). Option C is correct as for a dilation by a scale factor of 2, all corresponding sides should be in the ratio (2:1), and if (JK) and (ML) are not twice as long as (AB) and (DC), then it is not a dilation by a scale factor of 2.

Answer:

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