The coordinates of the point P on the directed line segment from A to B such that P is one-fourth the length of the line segment is P(x, y) = (- 2.75, - 0.5). (Right choice: C)
How to determine the coordinates of a point within a line segment
By geometry we remind that a line segment can be constructed from two distinct points on a plane. By linear algebra we can obtain an equation to determine the coordinates of a point within a line segment:
[tex]\vec P = \vec A + k \cdot \overrightarrow{AB}[/tex] (1)
Where:
- [tex]\vec A[/tex] - Coordinates of the point A.
- [tex]\vec P[/tex] - Coordinates of the point P.
- [tex]\overrightarrow {AB}[/tex] - Vectors between points A and B.
- [tex]k[/tex] - Length factor
If we know that A(x, y) = (- 5, - 1), B(x, y) = (4, 1) and k = 0.25, then the coordinates of the point P are:
P(x, y) = (- 5, - 1) + 0.25 · [(4, 1) - (- 5, - 1)]
P(x, y) = (- 5, - 1) + 0.25 · (9, 2)
P(x, y) = (- 5, - 1) + (2.25, 0.5)
P(x, y) = (- 2.75, - 0.5)
The coordinates of the point P on the directed line segment from A to B such that P is one-fourth the length of the line segment is P(x, y) = (- 2.75, - 0.5). (Right choice: C)
To learn more on line segments: https://brainly.com/question/25727583
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