Question

The line passing through the points $(3,-4)$ and $(-2,6)$ and a line passing through$(-3,6)$and $(9,-18)$ are

• A. Perpendicular
• B. Parallel
• C. Makes an angle$60°$ with each other
• D. None of these

Answer 1

The correct option is B

Parallel

Find the slope of the two lines

Given, points $(3,-4)$ and $(-2,6)$ and a line passing through$(-3,6)$and $(9,-18)$

The slope in two point form $=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}$

The slope $m_1$ of the line with points $(3,-4)$ and $(-2,6)$ is

$\Rightarrow m_1=\frac{\left(6-(-4)\right)}{\left(-2-\left(3\right)\right)}=-2$

The slope $m_2$ of the line with points $(-3,6)$and $(9,-18)$ is

$\Rightarrow m_2=\frac{\left(-18-6\right)}{(9+3)}=-2$

$\because m_1=m_2$, the slope of the lines are same

So, the lines are parallel

Hence, the option $B$ is the correct answer.