Question:

Determine if the lines passing through the given pairs of points are parallel, perpendicular or intersect obliquely.

(a) $\displaystyle (1,-1)$ , $\displaystyle (-4,-4)$ and $\displaystyle (1,1)$ , $\displaystyle (4,-4)$

(b) $\displaystyle (-6,-4)$ , $\displaystyle (22,8)$ and $\displaystyle (-5,7)$ , $\displaystyle (7,8)$

Attempt:

(a)

Slope of : $\displaystyle (1,-1)$ , $\displaystyle (-4,-4)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4-(-1)}{-4-1} = \frac{3}{5}$

Slope of : $\displaystyle (1,1)$ , $\displaystyle (4,-4)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4-1}{4-1} = -\frac{5}{3}$

The lines are perpendicular to each other. We can prove it by using $\displaystyle m_1 \times m_2 = -1$.

(b)

Slope of : $\displaystyle (-6,-4)$ , $\displaystyle (22,8)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-(-4)}{22 - (-6)} = \frac{3}{7}$

Slope of : $\displaystyle (-5,7)$ , $\displaystyle (7,8)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-7}{7-(-5)} = \frac{1}{12}$

It is an intersect obliquely.

Are my answers correct?