Question

What are the coordinates of the point on the directed line segment from (-1,-6) to (8, -3) that partitions the segment into the ratio 1:2 (or 1 to 2)?

A. (3, -5)
B. (2, -4)
C. (5, -4)
D. (6, -2)

Answer 1

The coordinates of the point that partitions the line segment into a ratio of 1:2 are approximately (4.6667, -5).

Step-by-step explanation:

To find the coordinates of the point that partitions the line segment into a ratio of 1:2, we can use the section formula. The section formula states that if we have two points A(x1, y1) and B(x2, y2) and we want to find the coordinates of a point P that divides the line segment AB in the ratio m:n, then the coordinates of P can be found using the formula:

P(x,y) = ((n * x1) + (m * x2))/(m + n), ((n * y1) + (m * y2))/(m + n)

In this case, the coordinates of point A are (-1,-6) and the coordinates of point B are (8,-3), and we want to divide the segment in a 1:2 ratio. Plugging these values into the formula, we get:

P(x,y) = ((2 * -1) + (1 * 8))/(1 + 2), ((2 * -6) + (1 * -3))/(1 + 2)

P(x,y) = (6 + 8)/3, (-12 - 3)/3

P(x,y) = 14/3, -15/3

Simplifying, we get P(x,y) = 4.6667, -5

So, the coordinates of the point that partitions the line segment into a ratio of 1:2 are approximately (4.6667, -5).