When point A(x_{1}, y_{1}) and point B(x_{2}, | vedclass

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(B) According to the section formula,if a point $P(x, y)$ divides the line segment joining points $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ in the ratio

Vedclass · Accepted Answer

$\left(\frac{\lambda x_{2}+x_{1}}{\lambda+1}, \frac{\lambda y_{2}+y_{1}}{\lambda+1}\right)$

Vedclass · Answer

(B) According to the section formula,if a point $P(x, y)$ divides the line segment joining points $A(x_{1}, y_{1})$ and $B(x_{2}, y_{2})$ in the ratio $m:n$,the coordinates of $P$ are given by:$x = \frac{mx_{2} + nx_{1}}{m + n}$$y = \frac{my_{2} + ny_{1}}{m + n}$Here,the ratio is given as $\lambda : 1$,so $m = \lambda$ and $n = 1$.Substituting these values into the formula:$x = \frac{\lambda x_{2} + (1)x_{1}}{\lambda + 1} = \frac{\lambda x_{2} + x_{1}}{\lambda + 1}$$y = \frac{\lambda y_{2} + (1)y_{1}}{\lambda + 1} = \frac{\lambda y_{2} + y_{1}}{\lambda + 1}$Thus,the coordinates are $\left(\frac{\lambda x_{2}+x_{1}}{\lambda+1}, \frac{\lambda y_{2}+y_{1}}{\lambda+1}\right)$.

When point $A(x_{1}, y_{1})$ and point $B(x_{2}, y_{2})$ are joined to form $\overline{AB}$ and a point divides $\overline{AB}$ in the ratio $\lambda : 1$,the coordinates of the point are:

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