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.Com
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)   (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 , 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 .

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

The point P has coordinates (a,b). Another point Q is formed by reversing the coordinates (answered by ikleyn)
Point A (-4,1) IS THE STANDARD (x,y) coordinate plane what must be the coordinate of... (answered by dabanfield)
Point A (-4, 1)is in the standard (x,y) coordinate plane. What must be the coordinate of... (answered by richwmiller)
Point A, which is (-4,1) is in the standard (x,y) coordinate plane. What must be the... (answered by solver91311)
Point A(-4,1) is in the standard (x,y) coordinate plane. What must be the coordinares of... (answered by solver91311)
point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of (answered by stanbon)
How do you solve: Point A (–4,1) is in the standard (x,y) coordinate plane. What must be (answered by dlam5)
Please help me with this Point A (-4,1) is in the standard (x,y) coordinate plane.... (answered by richwmiller,solver91311,stanbon)
Point A (-4,1) is in the standard (x,y) coordinate plane. What must be the coordinates of (answered by DrBeeee)