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.
0
Correct Answer: Option 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)