# Internal Division

## Internal Division of Line Segments

Internal Division an interval in a given ratio is that if the interval $(x_1,y_1)$ and $(x_2,y_2)$ is divided in the ratio $m:n$ then the coordinates are;
$$\Big(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\Big)$$

### Basic of Internal Division of Line Segments

If $A$ and $B$ are the points $(-4,3)$ and $(2,-1)$ respectively, find the coordinates of $P$ such that $AP:PB=3:1$.

### Negative Ratio of Internal Division of Line Segments

If $A$ and $B$ are the points $(-4,3)$ and $(2,-1)$ respectively, find the coordinates of $P$ such that $AP:PB=-4:5$.

### Three Equal Parts using Internal Division of Line Segments

Divide the interval between $(-1,1)$ and $(5,10)$ into three equal parts.

### Finding the Ratio of Internal Division of Line Segments

If the point $(-3,8)$ divides the interval between $(6,-4)$ and $(0,4)$ internally in the ratio $k:1$, find the value of $k$.