Question

If $\theta$ is the angle between the lines joining the points $A(0,0)$, $B(2,3)$ and the points $C(2,-2)$, $D(3,5),$ then the value of $\tan \theta$ is

• A. $\frac{17}{19}$
• B. $\frac{11}{19}$
• C. $\frac{17}{23}$
• D. $\frac{11}{23}$

Answer 1

The correct option is D $\frac{11}{23}$

Slope of $AB$
$m_1=\frac{3-0}{2-0}=\frac{3}{2}$
Slope of $CD$
$m_2=\frac{5+2}{3-2}=7$
So, $\tan \theta =\left|\frac{m_2-m_1}{1+m_1.m_2}\right|$
$=\left|\frac{7-\frac{3}{2}}{1+\frac{3}{2}\times 7}\right|\therefore \tan \theta =\frac{11}{23}$