Question

On a coordinates plane, a line passes through ( - 2 , 3 ) and ( 2 , 6 ). Which of the followings lies on the same line.

Answer 1

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

What point lies on a line segment?

According to linear algebra, a point lies in a line segment if its vector is a multiple of the vector that generates the line segment itself, that is:

AB = k · AP        (1)

The vector that generates the line segment is:

AB = (2, 6) - (- 2, 3)

AB = (4, 3)

And the vectors related to each point are:

Case A

AP = (- 2, 12) - (- 2, 3)

AP = (0, 9)

Case B

AP = (6, 12) - (- 2, 3)

AP = (8, 9)

Case C

AP = (- 6, 0) - (- 2, 3)

AP = (- 4, - 3)

Case D

AP = (- 6, 6) - (- 2, 3)

AP = (- 4, 3)

By direct comparison and definition of line segment  we notice that the point (x, y) = (- 6, 0) lies on the line segment AB as each AP is a multiple of former. (Correct choice: C)

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

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