Question

Derive a formula to find the angle between two lines with slopes m1 and m2 and state the conditions for two lines are parallel and perpendicular

Answer 1

Answer:

Step-by-step explanation:

If the two lines are parallel,

m1=m2

If the two lines are perpendicular,

m1=-1/m2

Answer 2

$tan\theta=\mid\frac{m_2-m_1}{1+m_2m_1}\mid$

When two lines are parallel then

$m_1=m_2$

When two lines are perpendicular then

$m_1=-\frac{1}{m_2}$

Step-by-step explanation:

Let slope of line 1=$m_1=tan\theta_1$

Slope of line 2=$m_2=tan\theta_2$

$\theta=\theta_2-\theta_1$

$tan\theta=tan(\theta_2-theta_1)$

We know that

$tan(x-y)=\frac{tanx-tany}{1+tanxtany}$

Using the formula

$tan\theta=\frac{tan\theta_2-\tan\theta_1}{1+tan\theta_2tan\theta_1}$

Substitute the values

$tan\theta=\frac{m_2-m_1}{1+m_1m_2}$

If $\frac{m_2-m_1}{1+m_2m_1}$ is positive then $tan\theta$ will be positive .

If $\frac{m_2-m_1}{1+m_2m_1}$ is negative then $tan\theta$ will be negative.

$tan\theta=\mid\frac{m_2-m_1}{1+m_2m_1}\mid$

Where $1+m_1m_2\neq 0$

When two lines are parallel then

$m_1=m_2$

When two lines are perpendicular then

$m_1=-\frac{1}{m_2}$

#Learns more:

https://brainly.in/question/7913915:answered by vivek 007146