Question

Coordinate plane with quadrilaterals ABCD and EFGH with A at (0, 0), B at (3, 0), C at (3, 2), D at (0, 2), E at (2, 4), F at (7, 4), G at (7, 0), and H at (2, 0). Are quadrilaterals ABCD and EFGH similar?

(a) No, quadrilaterals ABCD and EFGH are not similar because their corresponding segments are not proportional.
(b) 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.

Answer 1

Quadrilaterals ABCD and EFGH are not similar because their corresponding sides are not proportional, with side length ratios of 3/5 and 2/4 not being equivalent. Therefore, a translation and a dilation would not map ABCD onto EFGH.

Step-by-step explanation:

To determine whether quadrilaterals ABCD and EFGH are similar, we can examine the coordinates given for each vertex and compare the lengths of corresponding sides and the angles between them. For quadrilaterals to be similar, all corresponding sides must be proportional, and all corresponding angles must be congruent.

Quadrilateral ABCD has side lengths of 3 units (AB), 2 units (BC), 3 units (CD), and 2 units (DA). Quadrilateral EFGH has side lengths of 5 units (EF), 4 units (FG), 5 units (GH), and 4 units (HE). To have similarity, the side lengths of EFGH should be proportional to ABCD, which is not the case as the ratios are not equivalent (3/5 versus 2/4). Furthermore, a dilation from any point with a scale factor of 2 would double the lengths of the sides, not multiply them by 5/3 or 2. Therefore, the statement that quadrilaterals ABCD and EFGH are similar because a translation and dilation would map one onto the other is incorrect.

In conclusion, the answer to the question is (a) No, quadrilaterals ABCD and EFGH are not similar because their corresponding segments are not proportional.