Question

the image of trapezoid pqrs after a reflection across \\( \overleftrightarrow{wy} \\) is trapezoid pqrs.
what is \\( m \angle yxs \\)?
\\( 45 ^ { \circ } \\)
\\( 90 ^ { \circ } \\)
\\( 180 ^ { \circ } \\)
\\( 270 ^ { \circ } \\)

Explanation:

Step1: Recall the property of reflection

When a figure is reflected over a line, the line of reflection is the perpendicular bisector of the segment joining a pre - image point and its image point. In this case, \(\overleftrightarrow{WY}\) is the line of reflection.

Step2: Analyze the angle \(\angle YXS\)

The line of reflection \(\overleftrightarrow{WY}\) and the segment joining a point and its image (e.g., \(SS'\)) are related such that \(\angle YXS\) is formed by the intersection of the line of reflection and the segment joining a pre - image and its image. By the property of reflection, the line of reflection is perpendicular to the segment joining a pre - image and its image. A perpendicular angle has a measure of \(90^{\circ}\).

Answer:

\(90^{\circ}\)