­ In what ratio is the segment joining (12,­1) and (­3,4) divided by the Y ­axis?

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 (12,1) and (3,4) divided by the y-axis = $$k$$ : $$1$$

Since, the line segment is divided by y-axis, thus x coordinate of the point will be zero, let the point of intersection = $$(0,y)$$

Now, point P (0,y) divides (12,1) and (3,4) in ratio = k : 1

=> $$0 = \frac{(3 \times k) + (12 \times 1)}{k + 1}$$

=> $$3k + 12 = 0$$

=> $$k = \frac{-12}{3} = -4$$

$$\therefore$$ Line segment joining (12,­1) and (­3,4) is divided by the Y ­axis in the ratio = 4 : 1 externally

=> Ans - (A)