Question

The angle between the two lines $y-2x=9\text{and}x+2y=7,$ is

• A. $60°$
• B. $30°$
• C. $90°$
• D. $45°$

Answer 1

The correct option is C

$90°$

Explanation for the correct option:

Finding the angle between the two lines $y-2x=9\text{and}x+2y=7,$ is

Given: $y-2x=9\text{and}x+2y=7,$

$y=2x+9$

Comparing the above equation with $y=mx+c$ where $m$ is the slope of the equation

$\therefore m_1=2$

$$\begin{gathered} x+2y=7, \\ \Rightarrow y=-\frac{1}{2}x+7 \\ {m}_2=-\frac{1}{2} \end{gathered}$$

We know that the angle between two lines

$$\begin{gathered} \tan \theta =\left|\frac{(m_2–m_1)}{(1+m_1{m}_2)}\right| \\ =\left|\frac{\left({\displaystyle \frac{-1}{2}}–2\right)}{(1–1)}\right| \\ =\infty \\ \Rightarrow \theta =90°\left[\because tan90°=\infty \right] \end{gathered}$$

Hence the correct answer is option (C)