Hello, symmetry!

I must assume that you are familiar with the basic concepts needed:

. . slopes, perpendicular slopes, midpoints.

If you are not, learn or re-learn the formulas and concepts.

Show that the line containing the points and

is perpendicular to the line:

The slope of the line through and is: .

The slope of the line is: .

Since

Show that the midpoint of and lies on the line

The midpoint is: .

The two coordinates of the midpoint are equal.

. . Therefore, they satisfy the equation