Equation of a line passing through (1, –2) and perpendicular... | MATH - SLOPE OF LINE, EQUATION OF LINE IN | SolveeIt

Equation of a line passing through (1, –2) and perpendicular to the line $3 x - 5 y + 7 = 0$ is.

$5 x + 3 y + 1 = 0$

$3 x + 5 y + 1 = 0$

$5 x - 3 y - 1 = 0$

$3 x - 5 y + 1 = 0$

Answer

$5 x + 3 y + 1 = 0$

Explanation

Equation of a line perpendicular to $3 x - 5 y + 7 = 0$ is $5 x + 3 y + \lambda = 0$ ……(i)

This equation passes through $( 1 , - 2 )$

∴ $5 \times 1 + 3 \times ( - 2 ) + \lambda = 0$ ⇒ $5 - 6 + \lambda = 0$ ⇒ $\lambda = 1$

∴ Equation is $5 x + 3 y + 1 = 0$ .

Question: Equation of a line passing through (1, –2) and perpendicular to the line \(3 x - 5 y + 7 = 0\) is....