Show that the line containing the point (a, b) and (b, a) is perpendicular to the line y = x.
Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.
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