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 shortcut for division by an axis.
When the y-axis divides the segment joining $A(x_1, y_1)$ and $B(x_2, y_2)$, the ratio in which it divides the segment is simply $-x_1 : x_2$, since the dividing point has x-coordinate 0.
Step 2: Substitute the given coordinates.
Here $P(-4,-2)$ and $Q(10,4)$, so $x_1 = -4$ and $x_2 = 10$. The ratio is $-(-4) : 10 = 4 : 10$.
Step 3: Simplify the ratio.
Dividing both terms by 2, $4:10$ simplifies to $2:5$.
\[ \boxed{2:5} \]