Question

What are the coordinates of the point on the directed line segment from (-6, -3) to

(5,8) that partitions the segment into a ratio of 6 to 5?

Answer 1

Given:

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5.

To find:

The coordinates of that point.

Solution:

Section formula: If point divides a line segment in m:n, then the coordinates of that point are

`Point=\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

A point divides a directed line segment from (-6, -3) to (5,8) into a ratio of 6 to 5. Using section formula, we get

`Point=\left((6(5)+5(-6))/(6+5),(6(8)+5(-3))/(6+5)\right)`

`Point=\left((30-30)/(11),(48-15)/(11)\right)`

`Point=\left((0)/(11),(33)/(11)\right)`

`Point=\left(0,3\right)`

Therefore, the coordinates of the required point are (0,3).