The line determined by ( -4 , 3 ) and ( 6 , 3 ) has the slope
3-3
m = ------- = 0.
10
Normally the slope of a line perpendicular to one with slope m is the negative reciprocal of m. Here, however, the slope is zero, and the negative reciprocal of that does not exist. This signifies a VERTICAL line with undefined slope.
Thus, all we have to do to locate this line is to look at the x component of the given point thru which the line is to pass: That comp is 2.
Thus, the equation of the new line perpendicular to the old is x = 2.