Question

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)

Answer 1

0,6

Explanation:

Answer 2

(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)`