In what ratio Y-axis divides the line segment joining the points … - Vidyadip

Question

In what ratio Y-axis divides the line segment joining the points (3, 4) and (-2, 1) ?

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Answer

Let the given points be A(x₁, y₁) = (3, 4) and B(x₂, y₂) = (-2, 1). Let m : n be the ratio in which the line segment is divided by Y-axis (the co-ordinates of the point are (0, y)).
$\therefore$ $(0, y)=\left(\frac{m x_2+n x_1}{m+n}, \frac{m y_2+n y_1}{m+n}\right)$
⇒ $(0, y)=\left(\frac{-2 m+3 n}{m+n}, \frac{m+4 n}{m+n}\right)$
⇒ $0=\frac{-2 m+3 n}{m+n}$, and $y=\frac{m+4 n}{m+n}$
⇒ $-2 m+3 n=0$
⇒ $2 m=3 n$
⇒ $m: n=3: 2$

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