Answer: The required co-ordinate of point C is 3.
Step-by-step explanation: Given that the point C lies between the points A and B and the distance between points B and C is one-fourth of AB.
We are to find the co-ordinate of point C.
From the figure, we note that the co-ordinates of points A and B are -12 and 8 respectively.
Let x represents the co-ordinate of point C.
Then, according to the given information, we have
[tex]BC=\dfrac{1}{4}\times AB\\\\\\\Rightarrow 8-x=\dfrac{1}{4}(8-(-12))\\\\\Rightarrow 8-x=\dfrac{1}{4}20\\\\\Rightarrow 8-x=5\\\\\Rightarrow x=8-5\\\\\Rightarrow x=3.[/tex]
Thus, the required co-ordinate of point C is 3.
