To determine the line of reflection that will flip the trapezoid \( PQRS \) onto itself, you generally need to look for lines that are symmetrically equidistant from the vertices of the trapezoid.
For most trapezoids, particularly isosceles trapezoids, the line of reflection is typically the vertical line that runs through the midpoints of the bases. However, without the specific coordinates of points \( P \), \( Q \), \( R \), and \( S \), I cannot provide the exact equation for the line of reflection.
If we assume that \( PQRS \) is an isosceles trapezoid, the line of reflection could be \( x = k \), where \( k \) is the x-coordinate of the midpoint of the lengths of the parallel sides (the bases).
If the trapezoid is not isosceles or has different properties, the line of reflection might be \( y = c \) or could potentially be a different angle depending on the shape.
If you can provide specific coordinates or characteristics of the trapezoid, I can help find the precise line of reflection. Otherwise, a typical answer could be something like \( y = 0 \) (the x-axis) if the bases are oriented horizontally, or a vertical line if that is more applicable based on the trapezoid's shape.