Structural Integrity: Analyzing Normal and Parallel Support Segments

Structural Integrity: Analyzing Normal and Parallel Support Segments

\(A\) is the point \(\left( 2,5 \right)\) and the line joining the points \(A\) and \(B\) has a gradient of \(\frac{1}{3}\).

The perpendicular bisector of \(AB\) passes through the point \(\left( 4,9 \right)\). Find

  1. the equation of \(AB\),
  2. the coordinates of \(B\).

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Answer:\(\text{(a)}\hspace{0.5em}y=\dfrac{1}{3}x+\dfrac{13}{3}\) \(\text{(b)}\hspace{0.5em}B=(8,7)\)

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