Answer:
[tex]x=\dfrac{11}{3}[/tex]
Step-by-step explanation:
If points A, B, and C are collinear, then the slope between any two points will be consistent across all pairs. This is because all points lie on the same straight line, and the slope of a line is constant throughout.
[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope formula}}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\textsf{where:}\\\phantom{w}\bullet\;\;m\; \textsf{is the slope.}\\\phantom{w}\bullet\;\;(x_1,y_1)\;\textsf{and}\;(x_2,y_2)\;\textsf{are two points on the line.}\end{array}}[/tex]
To calculate the value of x, we can set the slopes of line segments AB and BC equal to each other:
[tex]\dfrac{y_B-y_A}{x_B-x_A}=\dfrac{y_C-y_B}{x_C-x_B}\\\\\\\\[/tex]
Given coordinates:
- [tex]x_A=-8[/tex]
- [tex]y_A=0[/tex]
- [tex]x_B=x-5[/tex]
- [tex]y_B=-8[/tex]
- [tex]x_C=x[/tex]
- [tex]y_C=-14[/tex]
Substitute the given coordinates into the equation and solve for x:
[tex]\dfrac{-8-0}{(x-5)-(-8)}=\dfrac{-14-(-8)}{x-(x-5)}\\\\\\\\\dfrac{-8}{x-5+8}=\dfrac{-14+8}{x-x+5}\\\\\\\\\dfrac{-8}{x+3}=\dfrac{-6}{5}\\\\\\\\-8\cdot 5=-6(x+3)\\\\\\-40=-6x-18\\\\\\6x=22\\\\\\x=\dfrac{22}{6}\\\\\\x=\dfrac{11}{3}[/tex]
Therefore, if points A, B and C are collinear, then the value of x is:
[tex]\Large\boxed{\boxed{x=\dfrac{11}{3}}}[/tex]
