Question

What are the coordinates of the point on the directed line segment from

(
1
,
2
)
(1,2) to
(
8
,
9
)
(8,9) that partitions the segment into a ratio of 6 to 1?

Answer 1

To find the coordinates of the point on the directed line segment that partitions the segment into a ratio of 6 to 1, we can use the following formula:

P = ( (6 * x2 + 1 * x1) / (6 + 1), (6 * y2 + 1 * y1) / (6 + 1) )

where P is the point we are looking for, (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment, and 6 and 1 are the ratio in which the segment is partitioned.

Substituting the given values, we get:

P = ( (6 * 8 + 1 * 1) / 7, (6 * 9 + 1 * 2) / 7 )

= ( 49 / 7, 60 / 7 )

= ( 7, 8.57 )

Therefore, the coordinates of the point on the directed line segment that partitions the segment into a ratio of 6 to 1 are (7, 8.57).