Question

In what ratio, Y-axis divides the line segment joining the points P(-4, 2) and Q(8, 3)?

• A. 3:1
• B. 1:3
• C. 2:1
• D. 1:2

Answer 1

The Correct Option is D

Let the Y-axis divide the line segment joining P(-4, 2) and Q(8, 3) in the ratio k:1. 

The coordinates of the point dividing the line segment are given by the section formula: $(\frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n})$ 

Here, m = k, n = 1, $(x_1, y_1) = (-4, 2)$, and $(x_2, y_2) = (8, 3)$. 

Since the Y-axis divides the line segment, the x-coordinate of the point of division is 0. 

$\frac{k(8)+1(-4)}{k+1}=0$ $8k - 4 = 0$ $8k = 4$ $k = \frac{4}{8} = \frac{1}{2}$ 

So the ratio is 1:2.