By direct comparison and definition of <em>line</em> segment we notice that the point (x, y) = (- 6, 0) lies on the <em>line</em> segment <u>AB</u> as each <u>AP</u> is a multiple of former. (Correct choice: C)
<h3>What point lies on a line segment?</h3>
According to linear algebra, a point lies in a <em>line</em> segment if its vector is a multiple of the vector that generates the <em>line</em> segment itself, that is:
<u>AB</u> = k · <u>AP</u> (1)
The vector that generates the <em>line</em> segment is:
<u>AB</u> = (2, 6) - (- 2, 3)
<u>AB</u> = (4, 3)
And the vectors related to each point are:
Case A
<u>AP</u> = (- 2, 12) - (- 2, 3)
<u>AP</u> = (0, 9)
Case B
<u>AP</u> = (6, 12) - (- 2, 3)
<u>AP</u> = (8, 9)
Case C
<u>AP</u> = (- 6, 0) - (- 2, 3)
<u>AP</u> = (- 4, - 3)
Case D
<u>AP</u> = (- 6, 6) - (- 2, 3)
<u>AP</u> = (- 4, 3)
By direct comparison and definition of <em>line</em> segment we notice that the point (x, y) = (- 6, 0) lies on the <em>line</em> segment <u>AB</u> as each <u>AP</u> is a multiple of former. (Correct choice: C)
To learn more more on line segments: brainly.com/question/25727583
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