Question

Find the equation of the straight line which divides the join of the points (2, 3) and (-5, 8) in the ratio 3 : 4 and is also perpendicular to it.

Answer 1

$\text{The coordinates of the point which divides the join of the points (2, 3) and (-5, 8) in the ratio 3 : 4 is given by (x, y) where,}x=\frac{l{x}^2+m{x}_1}{l+m}=\frac{3(-5)+4\left(2\right)}{3+4}=\frac{-15+16}{7}=\frac{-9}{7}y=\frac{l{y}_2+m{y}_1}{l+m}=\frac{3\left(8\right)+4\left(3\right)}{3+4}=\frac{24+12}{7}=\frac{36}{7}\text{Slope of the line joining the points}(2,3)and(-5,8)=\frac{8-3}{-5-2}=\frac{5}{-7}=\frac{-5}{7}\therefore \text{Slope of line perpendicular to line}=m=\frac{7}{5}\text{The required equation is :}y-y_1=m(x-x_1)y-\frac{36}{7}=\frac{7}{5}(x-\left(\frac{-9}{7}\right))49x-35y+229=0$