Question

Coordinate plane with quadrilaterals EFGH and E prime F prime G prime H prime at E 0 comma 1, F 1 comma 1, G 2 comma 0, H 0 comma 0, E prime negative 1 comma 2, F prime 1 comma 2, G prime 3 comma 0, and H prime negative 1 comma 0. F and H are connected by a segment, and F prime and H prime are also connected by a segment. Quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H'. Which characteristic of dilations compares segment F'H' to segment FH

Answer 1

Dilation by a scale factor of 2 means segment F'H' is twice as long as segment FH and the angles remain unchanged.

Step-by-step explanation:

The question asks about characteristics of dilations in geometry, specifically the comparison between segment FH and its dilation F'H'. When a figure is dilated using a scale factor, all linear dimensions (lengths of sides) are multiplied by the scale factor. In this case, quadrilateral EFGH was dilated by a scale factor of 2 from the center (1, 0) to create E'F'G'H', meaning every line segment on EFGH will be twice as long on E'F'G'H'. Therefore, segment F'H' is twice as long as segment FH.

Another important characteristic is that the angles between corresponding line segments are preserved during the dilation process. Since F and H, and F' and H' are connected by a segment, the angles between segment FH and the adjacent sides of EFGH should be the same as the angles between segment F'H' and the adjacent sides of E'F'G'H' due to the dilation.