Show that the line containing the points (a, b) and (b, a),
where a does not equal 0, is perpendicular to the line y = x.
Also, show that the midpoint of (a, b) and (b, a) lies on the line y = x.
You'll need to find the slope of the segment between (a, b) and (b, a).
Since the slopes are negative reciprocals of each other, the lines are perpendicular.
is the linear identity function. this means the x and y values are identical.
The midpoint between (a, b) and (b, a) can be found using the midpoint formula:
Since both x and y values of the midpoint are identical, then the midpoint has to lie on the identity function