In what ratio is the line segment joining the point (−2, −3) and (3, 7) divided by y-axis ?

Concept:

Let P and Q be the given two points (x1, y1) and (x2, y2) respectively, and M be the point dividing the line segment PQ internally in the ratio m : n, then from the section formula, the coordinate of the point M is given by:

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

Let point P be the point that lies at the y-axis and divide the line segment made by two points A and B in the ratio k : 1.

Since point P lies on the y-axis, therefore, the coordinates of the point P would be of the form (0, y).

Now, using the section formula and equating the x-coordinates, we get

\(0 = \frac{3k - 2}{k+1}\)

⇒ 3k - 2 = 0

⇒ k = 2/3

∴ k : 1 = 2 : 3

Hence, the required ratio is 2 : 3.