Question 550844
point B will be any point on the perpendicular bisector of AC.
as such it will be equidistant between A and C which will always make AB = BC.
the linear relationship is the equation of the line that passes through the midpoint of AC and is perpendicular to it.
the equation of the line AC is:
y = (3/5)x + (13/5)
the equation of the line perpendicular to AC and passing through its midpoint is:
y = -(5/3)x + 6
the graph of the equations for those line is shown below:
{{{graph(600,600,-15,15,-15,15,(3/5)x + (13/5),-(5/3)x+6)}}}
point B is any point on the line perpendicular to AC, so the linear relationship between the x value of that point and the y value of that point is the equation of the line perpendicular to AC which is the equation:
y = -(5/3)x + 6.
a picture of the relationship is shown below:
<img src = "http://theo.x10hosting.com/2011/dec291.jpg" alt = "$$$$$" />
line DE is perpendiculat to line AC.
any point on line DE is equidistant from A and C.