Question

In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the y-axis? Also, find the coordinates of the point of division.

Answer 1

Here y axis divides our line joined by the points (say) A (-2, -3) and B (3, 7). 

Let coordinate of the point be C(0, y). 

Here our x- coordinate is zero, as point C lie on x - axis. 

Let y axis divide AB in ratio of m:n.

By section formula

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

For point C(0, y) on line joined by the points A and B,

0 = \(\frac{m\times3 + n\times(-2)}{m + n}\).....(1)

And, y = \(\frac{m\times7 + n\times(-3)}{m + n}\)......(2)

Solving 1, 

0((m + n) = 3m – 2n 

∴ 3m = 2n 

∴m:n = 2:3 

Now solving for 2, for values m = 2 and n = 3,

y = \(\frac{2\times7 + 3\times(-3)}{2 + 3}\)

y = \(\frac{14 - 6}5\)

∴ y = \(\frac{5}5\) = 1

∴ C(0, y) ≡ (0, 1)