In what ratio does the point T (3,0) divide the segment joining the points S (4,­2) and U (1,4)?

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 S and U is divided by the point T = $$k$$ : $$1$$

Now, point T(3,0) divides S(4,2) and U(1,4) in ratio = k : 1

=> $$0 = \frac{(4 \times k) + (2 \times 1)}{k + 1}$$

=> $$4k + 2 = 0$$

=> $$k = \frac{-2}{4} = \frac{-1}{2}$$

$$\therefore$$ Line segment joining S and U is divided by T in the ratio = 1 : 2 externally

=> Ans - (B)