Question

What are the coordinates of point P on the directed line segment from A to B such that P is One-fourth the length of the line segment from A to B?

Answer 1

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:

$\vec P = \vec A + k \cdot \overrightarrow{AB}$     (1)

Where:

• $\vec A$ - Coordinates of the point A.
• $\vec P$ - Coordinates of the point P.
• $\overrightarrow {AB}$ - Vectors between points A and B.
• $k$ - 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: brainly.com/question/25727583

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