Q86 / 160 · TS EAMCET 2007 · Mathematics

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

A
$\pi$
Correct answer
B
$\pi / 2$
C
$\pi / 3$
D
$\pi / 6$

Solution

Given the line joining the points $(1,-2)(3,2)$ and $x+2 y-7=0$. Slope of the lines are $m_1=\frac{2+2}{3-1}=2 \quad$ and $\quad m_2=-\frac{1}{2}$ Now, $m_1 \times m_2=2 \times \frac{-1}{2}=-1$ $\therefore$ Lines are perpendicular, so angle is $\frac{\pi}{2}$.

Hence, the correct answer is option: 'B'.

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