Question

What are the coordinates of the point on the directed line segment from (-1, -8)(−1,−8) to (8, 4)(8,4) that partitions the segment into a ratio of 1 to 5?

Answer 1

The coordinates of the point on the directed line segment from (−1,−8) to (8,4) that partitions the segment into a ratio of 1 to 5 is
`((1)/(2), \hspace{0.1cm}-6)`.

Explanation:

To solve the question, we note that the difference in the x coordinate and the y coordinate of the line segment is as follows

(x₁, y₁) = (-1, -8), (x₂, y₂) = (8, 4)

Therefore, x₂ - x₁ = 8- (-1) = 9 An increase of 9 units

and y₁ - y₂ = 4 - (-8) = 12 An increase of 12 units

Also since we are looking for the point on the line that partitions the line in a ratio of 1 to 5, then we 1 portion of the line closer to the point (-1 -8) and 5 portions closer to (8, 4), making a total of 6 portions.

Therefore, the coordinates of the point is;

(-1 + 9×
`((1)/(6) )`, -8 + 12×
`((1)/(6) )` ) =
`((1)/(2), \hspace{0.1cm}-6)`.

The line segment is partitioned in a ratio 1 to 5 at point (1/2, -6).