Question

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

Answer 1

To find the value of P, we need to find the equation of each line and then examine the slopes of the lines.

The slope of the line joining (P, 4) and (6, -2) can be found using the slope formula:
slope = (y2-y1)/(x2-x1)
slope = (-2-4)/(6-P)
slope = -6/(6-P)

The slope of the line joining (2, P) and (-1, 3) can also be found using the slope formula:
slope = (3-P)/(-1-2)
slope = (3-P)/(-3)

Since the two lines are perpendicular, the product of their slopes will be -1:
(-6/(6-P)) * ((3-P)/(-3)) = -1

Multiplying both sides by -3 and 6-P, we get:
-6(3-P) = (-1)(-3)(6-P)
-18 + 6P = 9(6-P)
-18 + 6P = 54 - 9P

Adding 9P to both sides and adding 18 to both sides, we get:
15P = 72

Dividing both sides by 15, we get:
P = 72/15
P = 4.8

Since P must be a whole number, the value of P is 5.

Answer: D. 0