If the two lines with slope m_1 and m_2 are perpendicular then th… - Vidyadip

MCQ

If the two lines with slope $m_1$ and $m_2$ are perpendicular then their slopes has relation:

A
$m_1+m_2=1$
B
$m_1 \times m_2=1$
✓
$m_1 \times m_2=-1$
D
$m_1+m_2=-1$

✓

Answer

Correct option: C.

$m_1 \times m_2=-1$

$m_1 \times m_2=-1$

Solution:
If the two lines are perpendicular then if one line form angle $\alpha$ with positive x-axis then the other line form angle $90^\circ + \alpha$
If $\text{m}_{1} = \tan \alpha$ then $m_2$ will be $\tan (90^\circ + \alpha) = -\cot\alpha = \frac{-1}{\tan\alpha}$
$\Rightarrow m_1 \times m_2 = -1$.

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