Question

A friend of mine helped and said it was “Jeremy” who made the error but i don’t know why

Answer 1

Elisa made an error. She drew a 1 by 1 square. A square cannot be the image of a non-square preimage under a dilation.

Jeremy did fine. His rectangle is 1.5 times as wide and 1.5 times as tall as the original rectangle. So the proportions of the rectangles match: 4 by 6 and 6 by 9.

One thing that makes this problem tricky,I think, is that both of them used point B as the center of dilation, not the origin.

I am basing my conclusion using an assumption that ABCD and FGHJ are created such that F is the image of A, G is the image of B, and so on.

Answer 2

I don't think your friend is correct.

For each rectangle opposing corners are given, and conveniently the upper left corner is the same point as the original B (-3,3).

Jeremy's rectangle goes down to (3,-6) instead of (1,-3).  The new rectangle has a height of 3-(-6)=9 and a width of 3-(-3) = 6.  Compare that with the original rectangle with height 6 and width 4.  In this case each dimension is scaled up by the same factor (1.5), so it is a true enlargement of the original rectangle.

Elisa's rectangle on the other hand goes from (-3,3) to (-2,2), which just outlines the single square in the upper left of the original.  But that new rectangle is a square while the original was not, so this is clearly not a uniform rescaling of the original.  Indeed the height was reduced by 1/6 but the width only by 1/4.