Ab has endpoints at (-1, -1) and (-2, -4). its transformation a'b' has endpoints at (-2, -2) and (-4, -8). what type of transformation occurred? are lengths of segments affected by this type of transformation? justify.

A dilation has occurred.
Yes the length has been affected; specifically it has been doubled (twice as long).



Notice how the coordinates of (-1,-1) are doubled to get (-2,-2). Likewise when we go from (-2,-4) to (-4,-8). This shows us that we are dilating with a scale factor of 2, with the origin being the center of dilation. The scale factor 2 tells us that
new length = 2*(old length)

So the old figure is not going to be congruent to the new figure

To fully prove that the length has been doubled, you can use the distance formula to calculate the distance from (-1,-1) to (-2,-4) and that distance is sqrt(10) = 3.16 roughly

While the distance from (-2,-2) to (-4,-8) is 2*sqrt(10) = 6.32 roughly, so the distance has been doubled