Question

1. the rectangle abcd shown in the diagram below will be reflected across the x - axis. what will not be preserved? a. slope of \\( \overline { a b } \\) b. parallelism of \\( \overline { a b } \\) and \\( \overline { c d } \\) c. length of \\( \overline { a b } \\) d. measure of \\( \angle a \\)

Explanation:

Step1: Recall properties of reflection

Reflection is a rigid transformation. Rigid transformations preserve lengths (so length of \(\overline{AB}\) is preserved, eliminating option C), parallelism (so parallelism of \(\overline{AB}\) and \(\overline{CD}\) is preserved, eliminating option B), and angle measures (so measure of \(\angle A\) is preserved, eliminating option D).

Step2: Analyze slope

When a figure is reflected across the \(x -\)axis, the slope of a line segment changes sign. For example, if the slope of a line segment \(y = mx + b\) is \(m\), after reflection across the \(x -\)axis (\((x,y)\to(x, - y)\)), the new line segment has the equation \(y=-mx - b\) and slope \(-m\).

Answer:

A. slope of \(\overline{AB}\)