Answer:
the equation of the perpendicular bisector of segment AB is y = -2x + 7
Step-by-step explanation:
Going from B(-1, 4) to A(3, 6), x increases by 4 and y increases by 2. Thus, the slope of this line is m = rise / run = 2/4, or 1/2.
Any line perpendicular to the one joining A and B has a slope which is the negative reciprocal of 1/2: that'd be -2.
3 - 1 6 + 4
The midpoint of line segment AB is ( --------- , ---------- ), or (1, 5)
2 2
Thus, the perpendicular bisector passes through the midpoint (1, 5) and has slope -2:
Starting from y = mx + b, we get 5 = -2(1) + b, or 7 = b, and so the equation of the perpendicular bisector of segment AB is
y = -2x + 7
