Question

If L1 and L2 are two straight lines having slopes m1 and m2 respectively and m1 is perpendicular to m2 then prove that m1 * m2= - 1.

Answer 1

Answer:

M1 and M2 =90°

Sin90°= -1

prove it

Answer 2

Answer:

Concept:

Perpendicular lines are the lines that intersect each other at right angles (90 degrees)

Step-by-step explanation:

Refer to the image attached for obtaining the values of M1 and M2

                           $M_{1}=\tan \theta$

                            $& \quad m=\frac{\text { rise }}{run}$  $=\frac{\Delta y}{\Delta x }=\tan \theta$

                           $&M_{2}=\tan \left(90^{\circ}+\theta\right)$

                         We know that

                         $&\tan a=\frac{\sin a}{\cos a}$

                                  $&=\frac{\sin \left(90^{\circ}+\theta\right)}{\cos \left(90^{\circ}+\theta\right)}\\&=\frac{\sin 90 \cos \theta+\sin \theta \cos 90}{\cos 90 \cos \theta-\sin 90 \sin \theta}$

                                 $\begin{aligned}&=\frac{\cos \theta+0}{0-\sin \theta}=\frac{\cos \theta}{-\sin \theta} \\\\&\frac{\cos \theta}{-\sin \theta}=-\frac{1}{\left(\frac{\sin \theta}{\cos \theta}\right)}=\frac{-1}{\tan \theta}\end{aligned}$

                            $M_{2} =\frac{-1}{\tan \theta}$

                Now that we have the values of M1 and M2

                 By substituting M1 × M2 = -1

                                  =   $\frac{-1}{\tan \theta}\times tan\theta$

                                  = -1

                  Hence proved.

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