Bisector of an angle divides the opposite side in the ratio of the sides containing the angle.
Length of AB = \(\sqrt{(4-0)^2+(0-0)^2}=4\)
Length of AC = \(\sqrt{(0-0)^2+(3-0)^2}=3\)
So, the coordinates of the point P which divides the line joining (4, 0) and (0, 3) in the ratio 4 : 3.
BP : PC = 4 : 3, so coordinate of P is Coordinate of x
\(=4+\frac{4}{7}(0-4)=4-\frac{16}{7}=\frac{12}{7}\) Coordinate of y
\(=0+\frac{4}{7}(3-0)=0+\frac{12}{7}=\frac{12}{7}\)
Coordinate of P is \((\frac{12}{7},\frac{12}{7})\)
