On a coordinates plane, a line passes through ( – 2 , 3 ) and ( 2 , 6 ). Which of the followings lies on the same line.
a. ( – 2 , 12 )
b. ( 6 , 12 )
c. ( – 6 , 0 )
d. ( – 6 , 6 )

Answers

By direct comparison and definition of linesegment we notice that the point (x, y) = (- 6, 0) lies on the linesegmentAB 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 linesegment if its vector is a multiple of the vector that generates the linesegment itself, that is:

AB = k · AP(1)

The vector that generates the linesegment 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 linesegment we notice that the point (x, y) = (- 6, 0) lies on the linesegmentAB as each AP is a multiple of former. (Correct choice: C)

linesegmentwe notice that thepoint(x, y) = (- 6, 0) lies on thelinesegmentABas eachAPis a multiple of former. (Correct choice:C)## What point lies on a line segment?

linear algebra, apointlies in alinesegmentif itsvectoris a multiple of thevectorthat generates thelinesegmentitself, that is:AB= k ·AP(1)vectorthat generates thelinesegmentis:AB= (2, 6) – (- 2, 3)AB= (4, 3)vectorsrelated to eachpointare:Case AAP= (- 2, 12) – (- 2, 3)AP= (0, 9)Case BAP= (6, 12) – (- 2, 3)AP= (8, 9)Case CAP= (- 6, 0) – (- 2, 3)AP= (- 4, – 3)Case DAP= (- 6, 6) – (- 2, 3)AP= (- 4, 3)linesegmentwe notice that thepoint(x, y) = (- 6, 0) lies on thelinesegmentABas eachAPis a multiple of former. (Correct choice:C)line segments: https://brainly.com/question/25727583