What is the equation of the perpendicular bisector of the line segment connecting the points (2, 8) and (6, 4)?
y = x + 2
Step 1 – Midpoint: \(M = \left(\dfrac{{2+6}}{{2}}, \dfrac{{8+4}}{{2}}\right) = (4, 6)\)
Step 2 – Slope of segment: \(m_1 = \dfrac{{4-8}}{{6-2}} = -1\)
Step 3 – Slope of perpendicular bisector: \(m_2 = 1\) (negative reciprocal)
Step 4 – Equation through (4,6) with slope 1:
\(y - 6 = 1(x - 4) \Rightarrow y = x + 2\)
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