In what ratio does the point T(x, 0) divide the segment joining the points S(-4, -1) and U(1, 4)?

Solution (By Examveda Team)

$$\eqalign{ & \frac{{K\,\,\,\,\,:\,\,\,\,\,1}}{{S\left( { - 4,\, - 1} \right)\,\,\,\,\,\,\,\,\,\,T\left( {x,\,0} \right)\,\,\,\,\,\,\,\,\,\,U\left( {1,\,4} \right)}} \cr & \Rightarrow x = \frac{{k{x_2} + {x_1}}}{{k + 1}},\,\,y = \frac{{k{y_2} + {y_1}}}{{k + 1}} \cr & \Rightarrow 0 = \frac{{4k - 1}}{{k + 1}} \Rightarrow \boxed{k = \frac{1}{4}} \cr & {\text{Ratio }}\frac{1}{4}:1 = \boxed{1:4} \cr} $$