Question

Find the image of O (0,0) after two reflections, first across L1 and then across L2: L1: y = 2 L2: x = -3

Answer 1

Some standard rules:

`S_x(x,y)\rightarrow(x,-y+2k)` reflection about horizontal line y=k

`S_y(x,y)\rightarrow(-x+2h,y)` reflection about vertical line x=h

So for O(0,0), h=-3, k=2
First reflection about L1: y=2
(x,y)->(x, -y+2(k)) =>
O(0,0)->O'(0,-0+2(2) = O'(0,4)
Second reflection about L2: x=-3
(x,y)->(-x+2h,y) =>
O'(0,4)->O''(0+2(-3),4) = O"(-6,4)

Answer: after both reflections, the position of image is O"(-6,4)