Question 666156: Determine an equation for the right bisector of the line segment joining A(3,6) and B(-1,2).
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! There are two main components to this question. One component asks us to find a bisector of a line. This screams midpoint. The other asks that the bisector is right. In other words, the bisector forms a right angle with our line, and another way to think of this is that they are perpendicular. This means we need to find the slope of our line and then take its opposite reciprocal.
1) Find the slope of the line between (3,6) and (-1,2)
So the slope of our line is going to be the opposite reciprocal or -1.
In order for this line to be a bisector, it must contain the midpoint of our line.
The midpoint of (3,6) and (-1,2) = ((3+-1)/2 , (6+2)/2) = (2/2 , 8/2) = (1,4)
So we have a point (1,4) and a slope -1. Not surprisingly, we use the point-slope formula.
Reminder: y-y_1 = m(x-x_1) where (x_1,y_1) is a point and m is our slope.
y - 4 = -1(x-1)
y - 4 = -x + 1
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