Question 257290
Point A (-4,1) IS THE STANDARD (x,y) coordinate plane what must be the coordinate of point B so that the line x-2 is the perpendicular bisector of AB

The line y = x - 2 is in slope-intercept form so has a slope of 1. The line passing througth (-4,1) which is perpendicular to this line must have a slope which is the negative reciprocal of 1 which is -1/1 = -1. 

So the equation of the perpendicular line in slope-intercept form is

y = -1*x + b

Since (-4,1) is on this line we have:

1 = -1*-4 + b
b = -3

The equation of the perpendicular line is then:

y = -x - 3

To see where the two lines intersect we need to simulaneously solve:

1.) y = -x - 3
2.) y = x - 2  

Substitute x-2 in equation 1.):

x - 2 =  -x - 3
2x = -1
x = -1/2 (the x-coordinate of B)

Substitute -1/2 for x in 2.) above to get the value of y for point B.