Question

Find the coordinates of point P along the directed line segment AB, from B(6,1), so that the ratio of AP to PB is 3:2. The coordinates are:

(2, -1)
(3, -2)
(4, -2)
(5, -3)

Answer 1

To find the coordinates of point P along the directed line segment AB, we need to divide the segment into two parts based on the given ratio. Using the ratio of AP to PB, we can solve the equations to find the coordinates of point P.

Step-by-step explanation:

To find the coordinates of point P along the directed line segment AB, we need to divide the segment into two parts based on the given ratio. Let's assume the coordinates of point P are (x, y).

Using the ratio of AP to PB, we can set up the following equations:

(x-2)/(6-x) = 3/2

y-(-1)/(1-y) = 3/2

Solving these equations, we find that x = 4 and y = -2. Therefore, the coordinates of point P are (4, -2).