Find the coordinates of the vertices of a quadrilateral after reflection across the parallel lines; first across the x-axis and then across the line y = 1.

R (0,1), S (3,0), T (5,-4), Q (1,-3)

R' (0, 3), S' (3, 2), T' (5, - 2), Q' (1, - 1)

Step-by-step explanation:

The first reflection gives you the transformation ...

(x, y) ⇒ (x, - y)

The second reflection gives you the transformation ...

(x, y) ⇒ (x, 2 - y)

Applying the second transformation to the result of the first gives the overall transformation ...

(x, y) ⇒ (x, 2 - (-y)) = (x, 2+y)

That is, the double reflection is equivalent to a translation upward of 2 units. So, we add 2 to each y-value:

R' (0, 3), S' (3, 2), T' (5, - 2), Q' (1, - 1)