Question

type the correct answer in the box. use numerals instead of words. squares abcd and efch share a common center on a coordinate plane, as shown in the figure. (overline{eh}) is parallel to diagonal (overline{ac}). the number of lines of reflection about which the combined figure can reflect onto itself is

Explanation:

Step1: Analyze line of reflection for squares

A square has 4 lines of reflection: two diagonals and two lines through mid - points of opposite sides.

Step2: Consider the combined figure

Since \( \overline{EH}\parallel\overline{AC}\), the combined figure (squares \(ABCD\) and \(EFGH\) with common center) has 4 lines of reflection. These are the two diagonals of the larger square \(ABCD\) and the two lines passing through the mid - points of the sides of the larger square \(ABCD\) (which also act as lines of reflection for the combined figure due to the parallelism and common - center property).

Answer:

4