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 units on y axis.

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Solution

Slope $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{5 - 2}{3 - 1} = - 3$
Slope of a line perpendicular to the line $y = m x + c$ is $\frac{- 1}{m}$ with $y -$ intercept $3$ units.
$∴$ Slope of a line perpendicular to the line $y = m x + c$ is $\frac{- 1}{- 3} = \frac{1}{3}$ with $y -$ intercept $3$ units.
Thus, the required equation is $y = \frac{1}{3} x + 3$ or $3 y = x + 9$ or $x - 3 y + 9 = 0$

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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 units on y axis.

Slopem=y2−y1x2−x1=5−23−1=−3Slope of a line perpendicular to the line y=mx+c is −1m with y−intercept 3 units.∴ Slope of a line perpendicular to the line y=mx+c is −1−3=13 with y−intercept 3 units.Thus, the required equation is y=13x+3 or 3y=x+9 or x−3y+9=0

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 units on y axis.