In what ratio does the point T(x, 0) divide the segment joining the points S(5, 1) and U(-1, -2)?

Using section formula, the coordinates of point that divides line joining A = $$(x_1 , y_1)$$ and B = $$(x_2 , y_2)$$ in the ratio a : b

= $$(\frac{a x_2 + b x_1}{a + b} , \frac{a y_2 + b y_1}{a + b})$$

Let the ratio in which the segment joining (5,1) and (-1,-2) divided by the x-axis = $$k$$ : $$1$$

Now, point P (x,0) divides (5,1) and (-1,-2) in ratio = k : 1

=> $$0 = \frac{(-2 \times k) + (1 \times 1)}{k + 1}$$

=> $$-2k +1 = 0$$

=> $$k = \frac{-1}{-2} = \frac{1}{2}$$

$$\therefore$$ Required ratio = 1 : 2

=> Ans - (B)