Find the value of P if the line joining (P, 4) and (6, -2) is perpendicular to the line joining (2, P) and (-1, 3).
A. 4
B. 6
C. 3
D. O
Correct Answer: A
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.
\((\frac{-6}{6 - P})(\frac{3 - P}{-3}) = -1\)
\(\frac{6 - 2P}{6 - P} = -1 \implies 6 - 2P = P - 6\)
\(6 + 6 = P + 2P \implies P = \frac{12}{3} = 4\)
