Question

What is the angle between the lines x - 2y = 4 and y-3x + 7 = 0?
तिनत कति​

Answer 1

Answer:

$\huge\boxed{45^o=\dfrac{\pi}{4}}$

Step-by-step explanation:

The formula:

$y=m_1x+b_1;\ y=m_2x+b_2\\\\\tan\theta=\left|\dfrac{m_1-m_2}{1+m_1m_2}\right|$

We have

$x-2y=4;\ y-3x+7=0$

Convert to the slope-intercept form:

$x-2y=4\qquad|-x\\\\-2y=-x+4\qquad|:(-2)\\\\y=\dfrac{1}{2}x-2\to m_1=\dfrac{1}{2}\\=====================\\y-3x+7=0\\\\y=3x-7\to m_2=3$

Substitute

$\tan\theta=\left|\dfrac{\frac{1}{2}-3}{1+\left(\frac{1}{2}\right)(3)}\right|=\left|\dfrac{-2\frac{1}{2}}{1+\frac{3}{2}}\right|=\left|\dfrac{-\frac{5}{2}}{\frac{5}{2}}\right|=\left|-\dfrac{5}{2}\cdot\dfrac{2}{5}\right|=|-1|=1\\\\\tan\theta=1\to\theta=45^o=\dfrac{\pi}{4}$