Question

You'll need the other parts for part CPart CHow does the ratio of corresponding side lengths of the two quadrilaterals compare with the ratio of the areas of the quadrilaterals?

Answer 1

When the lengths increase by 2 times the area increases by 2².

C) We can see that from part A, and part B the ratio for the areas is:

`\begin{gathered} \frac{\:Area\:A^(\prime)B^(\prime)C^(\prime)D}{\:area\:ABCD^{\text{ }}}=(8)/(2)=4 \\ \\ (length\:A^(\prime)B^(\prime))/(length\:AB)=(2.83)/(1.41)\approx2 \end{gathered}`

2) So we can tell that when we dilate centered at the origin with a scale factor of 2 the area increases by (2)²=4

This is because the area is a square unit.