Question

The angle between the line joining the points $(1,-2),(3,2)$ and the line $x+2y-7=0$ is

• A. 0
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $\pi$

Answer 1

Answer: (C)

Slope of line passing through $(1,-2)$ and $(3,2)$ is
$m_1=\frac{2+2}{3-1}=2$
Slope of the line $x+2y-7=0$
$m_2=-\frac{1}{2}$
Now, $m_1{m}_2=2\times \frac{-1}{2}=-1$
$\therefore$ Angle between the line joining the points
$(1,-2)$ and $(3,2)$ and the line $x+2y-7=0$ is
$\frac{\pi }{2}$.