write the equation of the perpendicular bisector that goes through the line segment with end points of A -1,-2 and B -2,-8

Answer:   2x +12y = -63 . . . in standard form   y = -1/6x -21/4 . . . in slope-intercept formStep-by-step explanation:It is useful to find the midpoint of the segment. That is the average of the end points:   M = ((-1, -2) +(-2, -8))/2 = ((-1-2)/2, (-2-8)/2) = (-3/2, -5)It is also useful to find the changes in coordinates from B to A:   Δ = A-B = (-1-(-2), -2-(-8)) = (1, 6)From here, there are a couple of ways you can write the equation of the perpendicular line.__One way is to use the Δ values to compute the slope of the segment. The perpendicular line will have a slope that is the negative reciprocal of that.   Δy/Δx = 6/1 = 6   m = -1/6 . . . . . slope of the perpendicular lineNow we have a point and a slope for the desired line, so we can use a point-slope form of the equation for a line:   y = m(x -h) +k   y = (-1/6)(x -(-3/2)) +(-5)   y = (-1/6)x -21/4 . . . . . . . . eliminate parentheses; point-slope form__Another way to write the perpendicular line is to use the Δ values directly as coefficients in the standard form equation:   Δx(x -h) +Δy(y -k) = 0   1(x -(-3/2)) + 6(y -(-5)) = 0 . . . substitute values   x +6y +31.5 = 0 . . . . . . . . . . .collect terms   2x +12y = -63 . . . . . . . . . . . . multiply by 2, put in standard form