Question

Find the image of (1,2) after a

reflection about x = 6 followed by a
reflection about x = 4.

Answer 1

(-3,2)

Explanation:

When the point P(x,y) is reflected in the line
`x=k`, the mapping is

`P(x,y)\to P'(2k-x,y)`.

The image of (1,2) after a reflection about x = 6 is

`(1,2)\to (2*6-1,2)`.

`(1,2)\to (12-1,2)`.

`(1,2)\to (11,2)`.

When the resulting point is again reflected in the line x=4, we obtain

`(11,2)\to (2*4-11,2)`.

`(11,2)\to (8-11,2)`.

`(11,2)\to (-3,2)`.

Therefore the image of (1,2) after a

reflection about x = 6 followed by a

reflection about x = 4 is (-3,2)