Question

Find the equation of a line which is perpendicular to the line joining (4, 2) and (3, 5) and cuts off an intercept of length 3 on y-axis.

Answer 1

$\text{The required equation of line is y = mx + c}\text{Here, c = 3}\text{Let m be slope of the required line.}\text{Then,}m\times \text{slope of given line = - 1}\text{Slope of given line}\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{3-4}=\frac{3}{-1}=-3\Rightarrow m=\frac{1}{3}\text{So, the required equation is :}y=mx+cy=\frac{1}{3}x+3x-3y+9=0$