Find the image of A(4, -2) after it is reflected over the line y = 2, then reflected over the line x = 2. (-8, 6) (0, -2) (0, 6) (-8, -2)

Question

asked Dec 18, 2020 102k views

2 Answers

Mitchell Layzell · Answer 1 · 2020-12-24T02:52:21+0000

Answer:

(0, 6)

Explanation:

The given point A has coordinates (4,-2).

The mapping for a reflection over the line y=k, is given by:

$(x,y)\to (x,2k-y)$

Therefore the line y=2 is

$(4,-2)\to (4,2(2)--2)$

$(4,-2)\to (4,4+2)$

$(4,-2)\to (4,6)$

When this point is again reflected over the line x=2, we use the mapping

$(x,y)\to (2k-xx,y)$

$(4,6)\to (2(2)-4,6)$

$(4,6)\to (4-4,6)$

$(4,6)\to (0,6)$