Question

is figure abcd a reflection of figure abcd? explain. yes; it is a reflection over line f. no; it is not a reflection. yes; it is a reflection over the x-axis. yes; it is a reflection over the y-axis.

Explanation:

To determine if \( A'B'C'D' \) is a reflection of \( ABCD \), we analyze the transformation. A reflection over a line (the mirror line) means corresponding points are equidistant from the line and the line is the perpendicular bisector of the segment joining corresponding points. Here, line \( f \) (the diagonal line) acts as the mirror line: corresponding vertices of \( ABCD \) and \( A'B'C'D' \) are symmetric with respect to line \( f \). Reflections over the \( x \)-axis or \( y \)-axis would show symmetry across those axes, but the figure’s orientation matches reflection over line \( f \), not the axes. So it is a reflection over line \( f \).

Answer:

A. Yes; it is a reflection over line \( f \)