Question

Find the point P that is 2/5 of the way from A to B on the directed line segment AB if A (-8, -2) and B (6, 19).

Answer 1

The location of the point P that is 2/5 of the way from A to B on the directed line segment AB if A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).

How to determine the location of a point within a line segment

By geometry we know that a line segment is generated from two distinct points set on a plane. The location of the point P within the line segment can be found by means of the following vectorial formula:

P(x, y) = A(x, y) + k · [B(x, y) - A(x, y)], 0 < k < 1     (1)

Where:

• A(x, y) - Initial point
• B(x, y) - Final point
• k - Distance factor

If we know that A(x, y) = (- 8, - 2), B(x, y) = (6, 19) and k = 2/5, then the location of the point P is:

P(x, y) = (- 8, -2)  + (2/5) · [(6, 19) - (- 8, -2)]

P(x, y) = (- 8, -2) + (2/5) · (14, 21)

P(x, y) = (- 12/5, 32/5)

The location of the point P that is 2/5 of the way from A to B on the directed line segment AB if A(x, y) = (- 8, -2) and B(x, y) = (6, 19) is P(x, y) = (- 12/5, 32/5).

To learn more on line segments: https://brainly.com/question/25727583

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