The equation of the perpendicular bisector of the line segment joining the points (-3,8) and (-5,4) is y = mx + b. Find m+b. Note: The perpendicular bisector of the line segment \overline{AB} is the line that passes through the midpoint of \overline{AB} and is perpendicular to \overline{AB}.
+23246 The slope of the line segment whose endpoints are (-3,8) and (-5,4) is found by using the equation:
m = (y2 - y1) / (x2 - x1)
---> m = (4 - 8) / (-5 - -3) = -4 / -2 = 2
Therefore, the slope of the perpendicular is = -1/2
The midpoint of a line segment is found by the equation: midpt = ( (x1 + x2) / 2, (y1 + y2) / 2 )
= ( (-3 + -5) / 2, (8 + 4) / 2 ) = ( -8/2, 12/2 ) = ( -4, 6 )
If you know both the slope of a line and a point of the line, you can find the equation by using: y - y1 = m(x - x1)
y - 6 = (-1/2)(x - -4) ---> y - 6 (-1/2)(x + 4) ---> y - 6 = (-1/2)x - 2 ---> y = (-1/2)x + 4
Now, find m, b, and m + b.
