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.
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 = , y =
For point C(0, y) on line joined by the points A and B,
0 = …(1)
And, y = …(2)
Solving 1,
0(3m – 2n
∴ 3m = 2n
∴m:n = 2:3
Now solving for 2, for values m = 2 and n = 3,
y =
y =
∴ y = = 1
∴ C(0, y) ≡ (0, 1)