SOLUTION: In Rhombus ADBC, point A is (6,13) on the coordinate plane, and point B is (13,6) Find the slope-intercept equation of diagonal CD in the rhombus.

The rhombus could look like any of these, even the square on the right
(a square is a rhombus).  But regardless, the diagonal CD that goes up to
the right is always a segment of the same (green) line, and the green
line is always perpendicular to the red diagonal, because the diagonals
of a rhombus are perpendicular bisectors of each other.



We first find the slope of the red diagonal:

Slope formula
m =  with (x1, y1) = (6,13) and (x2, y2) = (13,6)

m =  =  = -1

The slope of the green line will have the slope that is formed by
inverting  as  or -1 and changing the sign to +1

So the slope of the desired green line is +1.

Now we need a point that it goes through.  Since the diagonals of any
parallelogram bisect each other, we must find the midpoint of the red
diagonal.

Midpoint formula:
 
Midpoint =  
 
Midpoint = 
 
Midpoint =    

Now we use the point-slope formula:

y - y1 = m(x - x1)

y -  = 1(x - )

y -  = x - 

     y = x

So that's the answer, the equation of the green line.

Edwin