Question

Given points A(-3,-2) and B(6,1), find the coordinates of point P on directed line segment BA that partitions BA in the ratio 1:2.

(a) (2,0)
(b) (3,0)
(c) (4,0)
(d) (5,0)

Answer 1

To find the coordinates of point P on the directed line segment BA that partitions BA in the ratio 1:2, we use the formula P(x,y) = (x1 + (1:2)(x2 - x1), y1 + (1:2)(y2 - y1)). Plugging in the coordinates of points A(-3,-2) and B(6,1), we find that the coordinates of point P are (6,1).

Step-by-step explanation:

To find the coordinates of point P on the directed line segment BA that partitions BA in the ratio 1:2, we first need to find the coordinates of point P. The coordinates of point P can be found using the formula:

P(x,y) = (x1 + (1:2)(x2 - x1), y1 + (1:2)(y2 - y1))

Plugging in the coordinates of points A(-3,-2) and B(6,1) into the formula, we get:

P(x,y) = (-3 + (1:2)(6 - -3), -2 + (1:2)(1 - -2))

Simplifying the equation, we get:

P(x,y) = (-3 + 9, -2 + 3) = (6, 1)

Therefore, the coordinates of point P are (6,1).