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…

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?\nyes, because sides j k and m l are twice as long as sides a b and d c.\nyes, because both figures are parallelograms, so corresponding sides are parallel.\nno, because sides j k and m l are not twice as long as sides a b and d c.\nno, because sides j m and k l have different slopes from sides a d and b c.

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?\nyes, because sides j k and m l are twice as long as sides a b and d c.\nyes, because both figures are parallelograms, so corresponding sides are parallel.\nno, because sides j k and m l are not twice as long as sides a b and d c.\nno, because sides j m and k l have different slopes from sides a d and b c.

Answer

Explanation:

Step1: Calculate the length of AB and JK

  • For side AB: Using the distance formula (d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}), if (A=(2,-2)) and (B=(4,-2)), then (AB=\sqrt{(4 - 2)^2+(-2+ 2)^2}=2)
  • For side JK: If (J=(4,-4)) and (K=(8,-4)), then (JK=\sqrt{(8 - 4)^2+(-4 + 4)^2}=4)

Step2: Check the scale - factor for other sides

  • For side DC: If (D=(1,-4)) and (C=(3,-4)), then (DC = 2)
  • For side ML: If (M=(3,-9)) and (L=(7,-9)), then (ML=4)
  • But for side AD: If (A=(2,-2)) and (D=(1,-4)), (AD=\sqrt{(2 - 1)^2+(-2 + 4)^2}=\sqrt{1 + 4}=\sqrt{5})
  • For side JM: If (J=(4,-4)) and (M=(3,-9)), (JM=\sqrt{(4 - 3)^2+(-4 + 9)^2}=\sqrt{1+25}=\sqrt{26}\neq2\sqrt{5})

A dilation requires all corresponding sides to be in proportion. Since not all sides of (JKLM) are twice the length of the corresponding sides of (ABCD) (e.g., (JM\neq2AD)), it is not a dilation by a scale - factor of 2.

Answer:

No, because sides (JK) and (ML) are not twice as long as sides (AB) and (DC) (the third option).