Question

soso nomework Assignment # 14 (i) On the grid at right, perform a glide-reflection by reflecting quadrilateral ABCD across the horizontal line Li and then translating its image horizontally 4 spaces to the left. C. (ii) If a point had coordinates (x,y), what would be the coordinates of its image under this glide-reflection?

Answer 1

i) coordinates of quadrilateral ABCD in matrix form can be written as A B C D 1 2 4 5 1 3 4 2 (2 unit spacing grid) Glide reflection Reflection about line L_1 and then translation of 4 spaces horizontally so, Transformation matrix for reflection about line L_1 will be T_1 = [1 0 0 - 1] and translation of 4 spaces horizontally will have translation matrix T_2 = [4 0 0 1] so, combined Translation matrix will be T = T_1 * T_2 T = [1 0 0 - 1][4 0 0 1] = [4 0 0 - 1] Therefore Glide - Reflection quadrilateral ABCD will be [1 2 4 5 1 3 4 2] [4 0 0 - 1] = [4 8 16 20 - 1 - 3 - 4 - 2] A* B* C* D* \r\n ii) If a point had co - ordinates (x, y) then its glide reflection will be [x y] [4 0 0 - 1] = [4x - y] Therefore (4x , - y)