Required raSOLVED EXAMPLESExample 1. Find the co-ordinates of the poin

1.	Required raSOLVED EXAMPLESExample 1. Find the co-ordinates of the point P which divides the line segment joiningA(8,9) and B(-7, 4), internally in the ratio 2 : 3.Clearly, y =The co-ord
Answer» We're GIVEN, $\longrightarrow \sf{A(8, 9) = ({x}_{1}, {y}_{1})}$ $\longrightarrow \sf{P = (\alpha, \beta)}$ $\longrightarrow \sf{B(-7, 4) = ({x}_{2}, {y}_{2})}$ $\longrightarrow \sf{AP:PB = m:n = 2:3}$ $\sf{\\ \\}$ We know by section formula, when a point $\sf{P(\alpha, \beta)}$ INTERSECTS internally a LINE segment AB where $\sf{A({x}_{1},{y}_{1})}$ and $\sf{B({x}_{2},{y}_{2})}$ in the ratio m : n, then:- $\quad \quad \longrightarrow \sf{\alpha = \dfrac{m{x}_{2} + n{x}_{1}}{m + n}}$ $\quad \quad \longrightarrow \sf{\beta = \dfrac{m{y}_{2} + n{y}_{1}}{m + n}}$ $\sf{\\ \\}$ So, putting the values, For alpha, $\longrightarrow \sf{\alpha = \dfrac{m{x}_{2} + n{x}_{1}}{m + n}}$ $\longrightarrow \sf{\alpha = \dfrac{(2 * -7) + (3 * 8)}{2 + 3}}$ $\longrightarrow \sf{\alpha = \dfrac{ - 14 + 24}{5}}$ $\longrightarrow \sf{\alpha = \dfrac{10}{5}}$ $\longrightarrow \underline{\sf{\alpha = 2}}$ $\sf{\\ \\}$ For beta, $\longrightarrow \sf{\beta = \dfrac{m{y}_{2} + n{y}_{1}}{m + n}}$ $\longrightarrow \sf{\beta = \dfrac{(2 * 4) + (3 * 9)}{2 + 3}}$ $\longrightarrow \sf{\beta = \dfrac{ 8 + 27}{5}}$ $\longrightarrow \sf{\beta = \dfrac{35}{5}}$ $\longrightarrow \underline{\sf{\beta = 7}}$ $\sf{\\ \\}$ Hence the ANSWER is, $\longrightarrow{\underline{\underline{\sf{ P = (2,7)}}}}$

Required raSOLVED EXAMPLESExample 1. Find the co-ordinates of the point P which divides the line segment joiningA(8,9) and B(-7, 4), internally in the ratio 2 : 3.Clearly, y =The co-ord

Answer»

$\longrightarrow \sf{A(8, 9) = ({x}_{1}, {y}_{1})}$

$\longrightarrow \sf{P = (\alpha, \beta)}$

$\longrightarrow \sf{B(-7, 4) = ({x}_{2}, {y}_{2})}$

$\longrightarrow \sf{AP:PB = m:n = 2:3}$

$\sf{\\ \\}$

We know by section formula, when a point $\sf{P(\alpha, \beta)}$ INTERSECTS internally a LINE segment AB where $\sf{A({x}_{1},{y}_{1})}$ and $\sf{B({x}_{2},{y}_{2})}$ in the ratio m : n, then:-