Question

the image of trapezoid pqrs after a reflection across w is trapezoid pqrs. what is m∠yxs? 45° 90° 180° 270°

Explanation:

Step1: Recall the property of reflection

A reflection across a line is a transformation. When a figure is reflected across 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, \(\overleftrightarrow{W}\) is the line of reflection.

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

Points \(Y\) and \(X\) lie on the line of reflection \(\overleftrightarrow{W}\). The line segment \(RS\) and its image \(R'S'\) are related by reflection across \(\overleftrightarrow{W}\). The angle between a segment and its image (when considering the line of reflection) for a non - parallel (to the line of reflection) segment and the line of reflection: If we consider the fact that the transformation is a reflection (a type of isometry), and looking at the orientation of the trapezoid and its image. A straight line has an angle measure of \(180^{\circ}\). The line \(\overleftrightarrow{W}\) is such that the angle between a segment (e.g., \(RS\) and its image \(R'S'\)) and the line of reflection: Since reflection is a rigid motion and the way the trapezoid is reflected, we know that \(\angle YXS = 90^{\circ}\) (because the line of reflection is perpendicular to the segment joining a point and its image (in the sense of the geometric transformation of reflection)).

So \(m\angle YXS=90^{\circ}\)

Answer:

B. \(90^{\circ}\)