## Division of a Line Segment

 7.1 Division of a Line Segment

 A point $$P(x,y)$$ that divides a line segment joining  $$A(x_1,y_1)$$ and $$B(x_2,y_2)$$ in the ratio of $$m:n$$ is given by

$$\boxed{P=\left(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n} \right)}$$

 For the case $$m=n$$, the point is a midpoint and is given by

$$\boxed{M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \right)}$$

 Example: Find the coordinates of point $$P$$ which divides the straight line $$AB$$ in the ratio $$AP:PB$$.

\begin{aligned} &A(-3,2),B(7,17);\\\\&AP:PB=2:3 \end{aligned}

\begin{aligned} P&=\left(\dfrac{2(7)+3(-3)}{2+3},\dfrac{2(17)+3(2)}{2+3} \right) \\\\ &= (1,8). \end{aligned}

## Division of a Line Segment

 7.1 Division of a Line Segment

 A point $$P(x,y)$$ that divides a line segment joining  $$A(x_1,y_1)$$ and $$B(x_2,y_2)$$ in the ratio of $$m:n$$ is given by

$$\boxed{P=\left(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n} \right)}$$

 For the case $$m=n$$, the point is a midpoint and is given by

$$\boxed{M=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2} \right)}$$

 Example: Find the coordinates of point $$P$$ which divides the straight line $$AB$$ in the ratio $$AP:PB$$.

\begin{aligned} &A(-3,2),B(7,17);\\\\&AP:PB=2:3 \end{aligned}

\begin{aligned} P&=\left(\dfrac{2(7)+3(-3)}{2+3},\dfrac{2(17)+3(2)}{2+3} \right) \\\\ &= (1,8). \end{aligned}