Find the value of P if the line joining (P, 4) and (6, -2) is…

Explanation

The line joining (P, 4) and (6, -2).

Gradient: \(\frac{-2 - 4}{6 - P} = \frac{-6}{6 - P}\)

The line joining (2, P) and (-1, 3)

Gradient: \(\frac{3 - P}{-1 - 2} = \frac{3 - P}{-3}\)

For perpendicular lines, the product of their gradient = -1.

\((\frac{-6}{6 - P})(\frac{3 - P}{-3}) = -1\)

\(\frac{6 - 2P}{6 - P} = -1 \implies 6 - 2P = P - 6\)

\(6 + 6 = P + 2P \implies P = \frac{12}{3} = 4\)

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