Question

show that two non vertical lines with slope m1 and m2 are perpendicular if and only if m1m2=-1


Who first answer my question correctly I will mark them as brainliest it's my promise

but the answer should be correct​

Answer 1

Step-by-step explanation:

Let the be 2 units L

1

,L

2

,mth slopes m

1

& m

2

such that

m

1

=tanθ

1

,m

2

=tanθ

2

Also, θ=θ

2

−θ

1

⇒tanθ=tan(θ

2

−θ

1

)

=

∣

∣

∣

∣

∣

1−tanθ

1

tanθ

2

tanθ

2

−tanθ

1

∣

∣

∣

∣

∣

- by formula

tanθ=

∣

∣

∣

∣

∣

1−m

1

m

2

m

1

−m

2

∣

∣

∣

∣

∣

---- (2)

Now, Given θ=

4

π

,L

1

:x−2y+5=0

⇒y=

2

x

+

2

5

[m

1

=

2

1

]

Putting in equation (1)

tan

4

π

=

∣

∣

∣

∣

∣

∣

∣

∣

1−

2

m

2

2

1

−m

2

∣

∣

∣

∣

∣

∣

∣

∣

⇒

∣

∣

∣

∣

1−

2

m

2

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

2

1

−m

2

∣

∣

∣

∣

∣

1−

2

m

2

=

2

1

−m

2

;1−

2

m

2

=−(

2

1

−m

2

)

⇒

2

m

2

=−

2

1

;

2

3

=

2

3

m

2

m

2

=−1,1