Question

The angle between the lines $x+2y=11$ and $2x-y=9$ is:

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

Answer 1

The correct option is C

$90°$

Step 1: Finding the slope of the given lines.

Given :

$x+2y=11......\left(1\right)$

$2x-y=9.....\left(2\right)$

Slope of $x+2y=11$ is

$$\begin{gathered} x+2y=11 \\ \Rightarrow y=-\frac{1}{2}x+\frac{11}{2}\left[\text{equation is of the form}y=mx+c\right] \\ \therefore m_1=\frac{-1}{2} \end{gathered}$$

Slope of $2x-y=9$ is

$$\begin{gathered} 2x-y=9 \\ \Rightarrow y=2x-9\left[\text{equation is of the form}y=mx+c\right] \\ \therefore m_2=2 \end{gathered}$$

Step 2: Finding the angle between the given lines.

Checking the relation between the two slopes by finding the product;

$m_1\times \mathbf{}{m}_2\mathbf{}=-\frac{1}{2}\times 2=-1$

Therefore, the lines are perpendicular to each other.

Hence the angle between the lines is $90°$.

Thus, the correct answer is Option (C).