Show that the lines $2 x + y + 1 = 0, x - 2 y + 1 = 0$ are perpendicular.

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Solution

First line $2 x + y + 1 = 0$
Slope $m_{1} = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f y} = \frac{- 2}{1} = - 2$
Second line is $x - 2 y + 1 = 0$
Slope $m_{2} = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f y} = \frac{- 1}{- 2} = \frac{1}{2}$
$∴ m_{1} \times m_{2} = - 2 \times \frac{1}{2} = - 1$
$∴$ Given lines are perpendicular.

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