Question

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)​

Answer 1

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

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)