Question

What are the coordinates of the point on the directed line segment from (-8,4) to (-3,9) that partitions the segments into a ratio of 3 to 2?

Answer 1

The coordinates of the point that partitions the line segment are (-1,6).

Step-by-step explanation:

To find the coordinates of the point that partitions the line segment from (-8,4) to (-3,9) in a ratio of 3 to 2, we need to use the section formula.

The section formula states that if the coordinates of two points are (x1,y1) and (x2,y2) and they divide the line segment in a ratio of m:n, then the coordinates of the partitioning point are

((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n)).

So, substituting the given values, we have:

((3*(-3) + 2*(-8)) / (3 + 2), (3*9 + 2*4) / (3 + 2))

Simplifying the expression, we get

(-1,6).