Question

Suppose the equation of line p is x = 2 and the equation of line q is x = –1. What translation is equivalent to rp ° rq rp ° rq = tŸ¨m, nŸ© where m = ___ and n = ___?

Answer 1

In the given transformation involving two reflections over vertical lines, the point translates horizontally by three units to the left, resulting in m = -3 and n = 0 in the translation function t٬m, n٩.

Step-by-step explanation:

The student's question involves finding the values of m and n in a translation transformation. Given the equations of line p being x = 2 and line q being x = –1, we are looking to understand the composite transformation described by rp ° rq rp ° rq, which suggests two reflections over the lines p and q. A reflection over the line x = a translates a point horizontally by 2a.

Reflecting over line q, x = -1, moves a point to the right by 2 units (since a is -1), putting it at x = 1. Another reflection over line p, x = 2, will translate it to the left by 4 units (since a is 2), putting the point at x = -2. As no vertical movement is involved, the translation represented by tʦm, nʨ has m = -3 and n = 0, because the point has moved 3 units to the left from its original position.