Question

Find the perpendicular bisector of the points A(3,6) and B(-1,4). Give your answer in the form

ax + by = c.​

Answer 1

the equation of the perpendicular bisector of segment AB is y = -2x + 7

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