Question

type the correct answer in the box. use numerals instead of words. squares abcd and efgh 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: Recall the properties of line of reflection

A line of reflection is a line such that when the figure is folded over this line, the two halves match exactly. For a square \(ABCD\), the lines of reflection are the two diagonals (\(\overline{AC}\) and \(\overline{BD}\)) and the two lines passing through the mid - points of opposite sides. But for the combined figure of \(ABCD\) and \(EFGH\) (where \(\overline{EH}\parallel\overline{AC}\)).

Step2: Analyze the symmetry

Since \(\overline{EH}\parallel\overline{AC}\), the lines of reflection for the combined figure are the two lines passing through the mid - points of opposite sides of the larger square \(ABCD\) (because of the parallel condition of the sides of the inner square \(EFGH\) with the diagonals of the outer square \(ABCD\)).

Answer:

\(2\)