Question

Find whether the lines drawn through the two pairs of points are parallel or perpendicular $(-1,-2),(1,6)$ and $(-1,1),(-2,-3)$.

Answer 1

Let $A(-1,-2),$ $B(1,6),$ $C(-1,1)$ and $D(-2,-3)$.

We know that the slope of the line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let us first find the slope of the line $AB$ with points $A(-1,-2)$ and $B(1,6)$ as shown below:

$m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{6-(-2)}{1-(-1)}=\frac{8}{2}=4$

Now, we find the slope of the line $CD$ with points $C(-1,1)$ and $D(-2,-3)$ as shown below:

$m_2=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-1}{-2-(-1)}=\frac{-4}{-1}=4$

We also know that if the slope of two lines are equal that is $m_1=m_2$, then the lines are parallel and

if the slope of the two lines have the relation $m_1\times m_2=-1$, then the lines are perpendicular to each other.

Here, since slope of the lines $AB$ and $CD$ are equal that is $m_1=m_2=4$

Hence, the line $AB$ is parallel to $CD$.