Question 91

# In what ratio is the segment joining points (2, 3) and (-2, 1) divided by the Y-axis?

Solution

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 (2,3) and (-2,1) 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 (2,3) and (-2,1) in ratio = k : 1

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

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

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

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

=> Ans - (B)