Triangle ABC is the pre-image and Triangle ADE is the image. What transformation took place?

a. Reflection
b. Translation
c. Dilation
d. Rotation

Dilation

Step-by-step explanation:

A dilation is a type of transformation that changes the size of the image. The scale factor measures how much larger or smaller the image is.

In this example, ΔABC is dilated as seen in the picture because it the picture itself got bigger.

The image, ΔADE is now a dilated version of the pre-image ΔABC

There is an attachment provided to support this answer.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.