Find the image of (1,2) after a reflection about x = 6 followed by a reflection about x = 4.

Question

asked Dec 21, 2020 153k views

1 Answer

Taurus Olson · Answer 1 · 2020-12-25T12:19:41+0000

Answer:

(-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)