The equation of the perpendicular bisector of BC with B(-2, 1), and C(4, 2) is y = 7.6 - 6•x
Which method can be used to find the equation of the perpendicular bisector?
The slope, m, of the line BC is calculated as follows;
- m = (2 - 1)/(4 - (-2)) = 1/6
The slope of the perpendicular line to BC is -1/(1/6) = -6
The midpoint of the line BC is found as follows;
[tex] \left( - 2 + \frac{4 - ( - 2)}{2}, \: 1 + \frac{2 - 1}{2} \right) = (1,\: 1.5)[/tex]
The perpendicular bisector is the perpendicular line constructed from the midpoint of BC.
The equation of the perpendicular bisector in point and slope form is therefore;
(y - 1.5) = -6•(x - 1)
y - 1.6 = -6•x + 6
y = -6•x + 6 + 1.6 = 7.6 - 6•x
Which gives;
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