Question

The line segment joining the points $P(-4, -2)$ and $Q(10, 4)$ is divided by y-axis in the ratio

• A. $2 : 5$
• B. $1 : 2$
• C. $2 : 1$
• D. $5 : 2$

Hint:

To find the ratio in which the $y$-axis divides the line segment joining $(x_1, y_1)$ and $(x_2, y_2)$, you can use the direct shortcut formula:
\[ \text{Ratio} = -x_1 : x_2 \]
Here, $-(-4) : 10 \implies 4 : 10 = 2 : 5$. This saves valuable time in multiple-choice questions!

Answer 1

The Correct Option is A

Step 1: Use the direct ratio shortcut for axis intersection.
When a segment joining $(x_1,y_1)$ and $(x_2,y_2)$ is cut by the $y$-axis, the ratio of division (from the first point) is $-x_1 : x_2$.
Step 2: Plug in the given coordinates.
Here $P(-4,-2)$ and $Q(10,4)$, so
\[ \text{Ratio} = -(-4) : 10 = 4 : 10 \]
Step 3: Simplify the ratio.
\[ 4 : 10 = 2 : 5 \]
Step 4: Conclude.
The $y$-axis divides $PQ$ in the ratio $2:5$, matching option (1).
\[ \boxed{2:5} \]