Hello, shenton,

the point P moves on the perpendicular bisector of the straight line from A(-4, 7) and B(3, -2).

1. Calculate the coordinates of the midpoint M of AB: M((-4+3)/2, (7-2)/2)

2. Calculate the slope of AB: (7-(-2))/(-4-3) = -9/7

3. The perpendicular direction is therefore: m = 7/9

Now you have a point and the slope of the line you are looking for. Use the point-slope-formula of a line:

(y - 5/2)/(x - (-1/2)) = 7/9 . Multiply by the denominator:

y - 5/2 = 7/9x + 7/18 Finally you get:

y = 7/9x + 26/9

EB