Question

Given a line segment that contains the points A,B, & C in order, if AB = x - 2, and BC = 2x + 6, and AC = 19, find x.
Select one:
a. 9
b. 11
c. 15
d. 5

Answer 1

Answer:

The answer to your question is: x = 5 units

Step-by-step explanation:

Data

AB = x - 2

BC = 2x + 6

AC = 19

x = ?

Process

                           AB + BC = AC

Solve for x,                        x - 2 + 2x + 6 = 19

                                           3x + 4 = 19

                                           3x = 19 - 4

                                           3x = 15

                                           x = 15 / 3

                                           x = 5 units

                                           

                       

Answer 2

The value of x is 5.

What is collinearity with three points?

Points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC, and CA is equal to the length of the remining line segment.

According to the given question.

Points A, B and C are collinear and point B lies in between A and C.

Also,

AB = x -2

BC = 2x + 6

AC = 19

Since, A, B and C are collinear points. Therefore, by collinearity

AC = AB + BC

⇒ $19 = x -2 + 2x + 6$

⇒$19 = 3x + 4$

⇒$19 - 4 = 3x$

⇒$15 = 3x$

⇒$x = 5$

Hence, option d is correct. That is the value of x is 5.

Find out more information about collinearity with three points here:

https://brainly.com/question/13069924

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