Question

Find the equation of straight line that passes through the point (1, 2) and perpendicular to the line 4x + 5y + 3 = 0.

• A. 5x - 4y + 3 = 0
• B. 4x + 5y + 3 = 0
• C. 5x - 4y + 9 = 0
• D. 5x - 4y + 5 = 0

Answer 1

The correct option is A

5x - 4y + 3 = 0

Equation of the line perpendicular to the line
4x+5y+9=0 is
5x-4y+$\lambda$ =0
This line passes through (1,2) $......\left(1\right)$
$5x^1-4x^2+\lambda$=0
5-8+$\lambda$=0
$\lambda =3$
Substituting $\lambda =3$ in equation 1
Equation of perpendicular line is 5x-4y+3=0

$\underset{–}{Alternativemethod}$
Slope of required line is perpendicular to the given line. So, product of slope of required line and given line = -1
$m_1.m_2=-1$
$\frac{-4}{5}.m_2=-1$
$m_2=\frac{5}{4}$
Equation of line with slope $\frac{5}{4}$ and passes through (1,2)
$y-2=\frac{5}{4}(x-1)$
4y-8=5x-5
5x-4y+3=0