Question

are quadrilaterals abcd and efgh similar?
no, quadrilaterals abcd and efgh are not similar because their corresponding segments are not proportional.
yes, quadrilaterals abcd and efgh are similar because a translation of (x + 3, y + 3) and a dilation by the scale factor of 2 from point a map quadrilateral abcd onto efgh.
no, quadrilaterals abcd and efgh are not similar because their corresponding angles are not congruent.
yes, quadrilaterals abcd and efgh are similar because a translation of (x + 2, y + 2) and a dilation by the scale factor of 2 from point d map quadrilateral abcd onto efgh.

Explanation:

Step1: Measure side lengths of ABCD

From the grid, side AB = 2, BC = 3.

Step2: Measure side lengths of EFGH

From the grid, side EH = 4, HG = 6.

Step3: Check side proportionality

Calculate ratios: $\frac{EH}{AB} = \frac{4}{2} = 2$, $\frac{HG}{BC} = \frac{6}{3} = 2$. All corresponding sides have equal ratios.

Step4: Check angle congruence

Both are rectangles, so all angles are $90^\circ$, congruent.

Step5: Verify transformation

Translation $(x+3, y+3)$ and dilation by scale factor 2 maps ABCD to EFGH.

Answer:

Yes, quadrilaterals ABCD and EFGH are similar because a translation of (x + 3, y + 3) and a dilation by the scale factor of 2 from point A' map quadrilateral ABCD onto EFGH.