Geo2.28

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The ratio in which the straight line L=ax+by+c=0\,divides the line joining the points A(x_1,y_1),B(x_2,y_2)\, is \frac{-L_[x_1,y_1]}{L_[x_2,y_2]}\,.


Let the straight line L=ax+by+c=0 divide the line joining A(x_1,y_1) B(x_2,y_2)\,

in the ratio l:m at P.

Since AP:PB=l:m

P=\left(\frac{lx_2+mx_1}{l+m},\frac{ly_2+my_1}{l+m}\right)\,

Point P lies on L=0, hence

a[\frac{lx_2+mx_1}{l+m}]+b[\frac{ly_2+my_1}{l+m}+c=0\,

Readjusting the variables

\frac{l}{m}=\frac{-(ax_1+by_1+c)}{ax_2+by_2+c}=\frac{-L_(x_1,y_1)}{L_(x_2,y_2)}\,


Main Page:Geometry:Straight Lines-I

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