Question

is the line through points p (-9,-10) and q (-15,-17) perpendicular to the line through points r (-5,-2) and s (-11,5)

Answer 1

Perpendicular lines have opposite slopes.
Ex.
if one slope is 4/3, the other slope will be -3/4.
So you need to find the slope of both lines.

Answer 2

Use the formula (y1-y2)/(x1-x2) to find the slope.

Answer 3

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
P&({\color{red}{ -9}}\quad ,&{\color{blue}{ -10}})\quad Q&({\color{red}{ -15}}\quad ,&{\color{blue}{ -17}})\\
R&({\color{red}{ -5}}\quad ,&{\color{blue}{ -2}})\quad S&({\color{red}{ -11}}\quad ,&{\color{blue}{ 5}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\)

find their slopes... if one is the NEGATIVE RECIPROCAL of the other as already pointed out by hlambach