Question

If point p (6,9) is reflected across the line y =2, what are the coordinates of its reflection image

Answer 1

the answer is (4,11) try using desmos.com for problems like these

Answer 2

we know that

The point Q is the image of point P in the line mirror, such that PQ is perpendicular to the line mirror, and the mid point L of PQ lies on the line mirror

So

In this problem the line mirror is equal to

`y=2`

point P is
`(6,9)`

PQ is perpendicular to
`y=2`

PQ is equal to
`x=6`

the midpoint L is
`(6,2)`

the distance point L to point P is equal to

`(9-2) = 7\ units`

the distance point L to point Q will be also
`7\ units`

the coordinates of point Q is equal to

`(6,2-7)= (6,-5)`

therefore

the answer is

`Q(6,-5)`

see the attached figure to better understand the problem