Find the ratio in which the join of (-4, 7) and (3, 0) is divided by the y-axis. Also, find the co-ordinates of the point of intersection.

Let the point on y-axis be (0, y) and required ratio be k : 1.

By formula,

$x = \dfrac{m$1x2 + m2x1}{m1 + m2}

Substituting values we get,

$\Rightarrow 0 = \dfrac{k \times 3 + 1 \times -4}{k + 1} \\[1em] \Rightarrow 0 = 3k - 4 \\[1em] \Rightarrow 3k = 4 \\[1em] \Rightarrow k = \dfrac{4}{3}.$

k : 1 = $\dfrac{4}{3} : 1 = 4 : 3$.

$y = \dfrac{m$1y2 + m2y1}{m1 + m2}

Substituting values we get,

$\Rightarrow y = \dfrac{4 \times 0 + 3 \times 7}{4 + 3} \\[1em] \Rightarrow y = \dfrac{0 + 21}{7} \\[1em] \Rightarrow y = 3.$

P = (0, y) = (0, 3).

Hence, ratio = 4 : 3 and co-ordinates of point of intersection = (0, 3).