Answer: The answer is 12.
Step-by-step explanation: Given that a point 'x' is lying at [tex]\dfrac{2}{3}[/tex] on the number line. Another point 'y' is also lying at the same distance from 0 but has a numerator of 8. We are to find the denominator of 'y'.
Since 'x' is lying at [tex]\dfrac{2}{3}[/tex] on the number line so its distance from 0 will be
[tex]d_x=\dfrac{2}{3}-0=\dfrac{2}{3}.[/tex]
Let the denominator of 'y' be p, then its distance from 0 will be
[tex]d_y=\dfrac{8}{p}-0=\dfrac{8}{p}.[/tex]
According to the given information, we must have
[tex]d_x=d_y\\\\\\\Rightarrow \dfrac{2}{3}=\dfrac{8}{p}\\\\\\\Rightarrow p=\dfrac{8\times 3}{2}=12.[/tex]
Thus, the denominator will be 12.
