SOLUTION: A (x,y) is a point on the number plane. B is formed by reversing the coordinate of A. Show that AB is perpendicular to the line y=x and show that the midpoint C of AB which is lyin

Algebra ->  Graphs -> SOLUTION: A (x,y) is a point on the number plane. B is formed by reversing the coordinate of A. Show that AB is perpendicular to the line y=x and show that the midpoint C of AB which is lyin      Log On


   

Question 1024483: A (x,y) is a point on the number plane. B is formed by reversing the coordinate of A. Show that AB is perpendicular to the line y=x and show that the midpoint C of AB which is lying on y=x.
How do I do this? Please explain
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The described process follows the definition of function inverse.


x y pair (p,r).
Switching the x and y values gives the point (r,p).
Slope of these two points is %28p-r%29%2F%28r-p%29=%28-1%29%28r-p%29%2F%28r-p%29=highlight_green%28-1%29, and this is for the line connecting (p,r) and (r,p).

The other line referenced, y=x which can be taken as being in slope-intercept form, has obviously the slope highlight_green%281%29.

Notice that the product of the slopes for (p,r) to (r,p) and line y=x is -1%2A1=-1. The product of two slopes being NEGATIVE ONE, means that the lines are PERPENDICULAR.