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The coordinates of the point P on the directed <em>line</em> segment from A to B such that P is one-fourth the length of the <em>line</em> segment is P(x, y) = (- 2.75, - 0.5). (Right choice: C)
<h3>How to determine the coordinates of a point within a line segment</h3>
By geometry we remind that a <em>line</em> 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 <em>line</em> segment:
(1)
Where:
- Coordinates of the point A.
- Coordinates of the point P.
- Vectors between points A and B.
- 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 <em>line</em> segment from A to B such that P is one-fourth the length of the <em>line</em> segment is P(x, y) = (- 2.75, - 0.5). (Right choice: C)
To learn more on line segments: brainly.com/question/25727583
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