Question

Find the equation of the line passing through the point (-3, 5) and perpendicular to the line joining (2, 5) and (-3, 6).

Answer 1

$\text{The line passes through the point (-3, 5)}$

$So(x_1,y_1)=(-3,5)$

$\text{The line is perpendicular to the line joining (2, 5) and (-3, 6)}$

$\Rightarrow m=\frac{-1}{\text{slope of line joining (2, 5) and (-3, 6)}}$

$=\frac{-1}{\frac{y_2-y_1}{x_2-x_1}}=\frac{-1}{\frac{6-5}{-3-2}}=\frac{-1}{\frac{-1}{5}}$

$\therefore m=5$

$\text{Hence, equation of straight line is}$

$y-y_1=m(x-x_1)$

$y-5=5\left\{x\right(-3\left)\right\}$

$y-5=5(x+3)$

$y-5=5x+155x-y+20=0$