Question

the image of trapezoid pqrs after a reflection across
\\( \overleftrightarrow { wy } \\) is trapezoid \\( p ^ { \prime } q ^ { \prime } r ^ { \prime } s ^ { \prime } \\).
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 across a line, the line of reflection is the perpendicular bisector of the segment joining a point and its image. Here, \( \overleftrightarrow{WY}\) is the line of reflection. So, \( \angle YXS = 90^{\circ}\) because the line of reflection is perpendicular to the segment joining a pre - image and its image.

Answer:

\(90^{\circ}\) (the second option)