Let the line m be given by x 6 and let the line k be given

Let the line m be given by x = 6 and let the line k be given by x = 10. Find the image of the point A = (x,y) under the translation given by rk rm.

Let the line m be given by x 6 and let the line k be given by x 10. Find the image of the point A (x, y) under the translation given by o

Solution

[Note: Instead of translation operation, it should be reflection]

In the composition operation r_k r_m. first r_m will apply on A then it follow the operation of r_k.

The reflection of point A(x, y) about the line m (x = 6) will result in image coordinates A\' (12-x, y).

Thus, r_m A(x,y) = A\' (12 - x, y) and

The reflection of point A\' (12 - x, y) about the line k (x = 10) will result in image coordinates A\'\' (20-(12-x), y).

Thus, (r_k r_m) A(x,y) = r_k (A\' (12 - x, y)) = A\'\' (8+x, y)