Coordinates of a point dividing a line segment in a given ratio

Question

In the figure BP is bisector of angle B if BC=2AB and A(1,2) and C(-2,-4) find coordinates of P I found K which is equal to 2 but for finding coordinates of P we need to use formula which is (x1+k(x2)/k+1 and is the same for y But which one do we take as x1 {1 or -2} and how can we identify x1 and x2

Answer 1

$\frac{BC}{BA}=\frac{CP}{PA}=2=k$, where $C(x_1;y_1)$ (first point in numerator) and $A(x_2;y_2)$ (second point in denominator).

In the example $x=\frac{-2+2\cdot 1}{2+1}=0$, $y=\frac{-4+2\cdot 2}{2+1}=0$.