Question

Is the line through points P(2,-9) and Q(6, -13) perpendicular to the line through points R(5,-1) and
S(1,-5)?

Answer 1

Two lines $y_1,y_2$ are perpendicular if their slopes are in a relation $m_1=-\frac{1}{m_2}$.

So we need to find slopes and if the above relation holds then we can claim the lines are perpendicular.

To find slopes, use slope formula

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

The first slope of a line passing through $PQ$ is

$m_1=\frac{-13-(-9)}{6-2}=\frac{-4}{4}=-1$

The second slope of a line passing through $RS$ is

$m_2=\frac{-1-(-5)}{5-1}=\frac{4}{4}=1$

Now check if $m_1=-\frac{1}{m_2}$ is true

$-1=-\frac{1}{1}\implies -1=-1$

This means the two lines are perpendicular.

Hope this helps.