Question

One line passes through the points $(1,9)$ and $(2,6)$ another line passes through $(3,3)$ and $(-1,5)$ The acute angle between the two lines is

• A. 30${}^{\circ }$
• B. 45${}^{\circ }$
• C. 60${}^{\circ }$
• D. 135${}^{\circ }$

Answer 1

The correct option is B 45${}^{\circ }$

Slope of line passing through $(1,9)$ and $(2,6)$ is

$m_1=\frac{6-9}{2-1}$

$=\frac{-3}{1}$

$=-3$

$=>tan{\theta }_1=-3$

$=>{\theta }_1=ta{n}^{-1}(-3)$

$=-{71.57}^0$

Slope of line passing through $(3,3)$ and $(-1,5)$ is

$m_2=\frac{5-3}{-1-3}$

$=\frac{-2}{4}$

$=\frac{-1}{2}$

$=>tan{\theta }_2=\frac{-1}{2}$

$=>{\theta }_2={tan}^{-1}\frac{-1}{2}$

${\theta }_2=-{26.57}^0$

Angle between them $=-{26.57}^0+{71.57}^0$

$={45}^0$