Segment j k has coordinates j begin ordered pair 3 comma negative 6 end ordered pair and k begin ordered pair negative 3 comma 2 end ordered pair. when segment j k is dilated with a scale factor negative 4, what are the coordinates of j prime and k prime?

We write the coordinates of J and K:
 J = (3, -6)
 K = (- 3, 2)
 The coordinates of J and K applying a scale factor k = -4 will be:
 J '= k * (3, -6) = - 4 * (3, -6)
 K '= k * (- 3, 2) = - 4 * (- 3, 2)
 Rewriting:
 J '= (- 4 * 3, -4 * (- 6)) = (-12, 24)
 K '= (- 4 * (- 3), -4 * 2) = (12, -8)
 
 The coordinates of J prime and K prime are:
 J '= (-12, 24)
 K '= (12, -8)

The length of each side of each leaf is about 5.7.

I assume the the side you are looking for is the outside diagonal side.

To find this, you can use the Pythagorean Theorem for half the distance.

2^2 + 2^2 = c^2
4 + 4 = c^2
8 = c^2
2.828 = c

Now, multiply this by 2 because we only found half of the complete side.
The length is about 5.7 units.