In what ratio does the y-axis divide the line segment joining the points (-3, -4) and (1, 2)?

Given -

The coordinates of the points are:

Point A: (-3, -4) and Point B: (1, 2)

Concept -

The formula to find the coordinates where a line segment is divided by a point (x, y) in the ratio m:n is:

\(\left(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}\right) \)

Explanation -

Here, the y-axis intersects the line segment AB at some point (0, y). Let's denote the ratio in which the y-axis divides AB as m:n.

For the y-axis to intersect at (0, y), the x-coordinate will be 0.
Using the section formula:

\( \left(\frac{n \cdot (-3) + m \cdot 1}{m + n}, \frac{n \cdot (-4) + m \cdot 2}{m + n}\right) = (0, y)\)

From this, we get the following equations:

\( \frac{-3n + m}{m + n} = 0 \\ \frac{-4n + 2m}{m + n} = y \)

From the first equation, we get m = 3n.

Substitute m = 3n into the second equation:

\( \frac{-4n + 2(3n)}{3n + n} = y \\ \frac{-4n + 6n}{4n} = y \\ \frac{2n}{4n} = y \\ y = \frac{1}{2} \)

Therefore, the y-axis divides the line segment joining (-3, -4) and (1, 2) in the ratio 3:1.