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)

Answer 2

Answer:

the answer is (-6, -4) (i think)

Step-by-step explanation:

the answer for L1 is (0, -4) and the answer for L2 is (-6, 0)

those two put together is (-6, -4)

hope this helps :)