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Mrrafil [7]
3 years ago
5

Write an equation of the perpendicular bisector of the segment with end points M(1,5) and N(7,-1)

Mathematics
1 answer:
vitfil [10]3 years ago
4 0
The perpendicular bisector of the segment passes through the midpoint of this segment. Thus, we will initially find the midpoint P:

P=\dfrac{(1,5)+(7,-1)}{2}=\dfrac{(8,4)}{2}=(4,2)

Now, we will calculate the slope of the segment support line (r). After this, we will use the fact that the perpendicular bisector (p) is perpendicular to r:

m_r=\dfrac{\Delta y}{\Delta x}=\dfrac{5-(-1)}{1-7}=\dfrac{6}{-6}\iff m_r=-1


p\perp r\Longrightarrow m_p\cdot m_r=-1\Longrightarrow m_p\cdot(-1)=-1\iff m_p=1

We can calculate the equation of p by using its slope and its point P:

y-y_P=m_p(x-x_P)\\\\
y-2=1\cdot(x-4)\\\\
y-2=x-4\\\\
\boxed{p:~~y=x-2}
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