The line segment joining the points (4, -5) and (-1, 2) is divided by the Y-axis.
The point which divides the given line segment. lies on Y-axis.
Its abscissa is 0.
Let the point (0, y) intersects the line segment joining the point (4, -5) and (-1, 2) in the ratio m : n.
Using Section formula, we have.
\(x=\frac{m x_2+n x_1}{m+n} ; \) \(y=\frac{m y_2+n y_1}{m+h} \)
\(x=\frac{m x_2+n x_1}{m+n} ; \)
\( 0=\frac{m \times(-1)+n(4)}{m+n} ; \)
\( 0=\frac{-m+4 n}{m+n} \)
\(-m+4 n=0 \)
\(-m = -4 n\)
\(\frac {m}{n} = \frac {4}{1}\)
m : n = 4 : 1
\(\text {This implies, } y=\frac{m y_2+n y_1}{m+n}\)
\(=\frac{4 \times 2+1 \times(-5)}{4+1} \)
\( =\frac{8-5}{5}\)
\(=\frac {3}{5}\)
The ratio of division is 4 : 1 and the Coordinates of the point of division are \((0,\frac {3}{5})\).
