Question

Find the image of (1, 2) after a reflection about x= 3 followed by a reflection about x= 7.

Please Help!!!

Answer 1

(9, 2 )

Explanation:

Under a double reflection in 2 parallel vertical lines

The y- coordinate remains unchanged

The x- coordinate is twice the difference of the parallel lines added to the original x- coordinate, that is

image = (1 + 2(7 - 3), 2 ) = (1 + 8, 2) = (9, 2 )

Answer 2

(9,2)

Explanation:

(1,2) is reflected over vertical line x=3 which means since (1,2) is 2 units over from x=3 that the reflection is going to be 2 units over in the other direction from x=3 so the first image is (5,2)

Now the last image is processed by a reflection through vertical line x=7

(5,2) is 2 units from x=7 so the reflection will also be 2 units from the vertical line x=7 so the final image is (9,2).

Answer (9,2)