A)
[tex]\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
P&({{ -1}}\quad ,&{{ 7}})\quad
% (c,d)
R&({{ 3}}\quad ,&{{ 8}})
\end{array}\qquad
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[3-(-1)]^2+[8-7]^2}\implies d=\sqrt{(3+1)^2+(8-7)^2}
[/tex]
B)
[tex]\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
P&({{ -1}}\quad ,&{{ 7}})\quad
% (c,d)
Q&({{ 0}}\quad ,&{{ -5}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-5-7}{0-(-1)}\implies \cfrac{-5-7}{0+1}[/tex]
C)
[tex]\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
Q&({{ 0}}\quad ,&{{ -5}})\quad
% (c,d)
R&({{ 3}}\quad ,&{{ 8}})
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left(\cfrac{{{ 3}} + {{0}}}{2}\quad ,\quad \cfrac{{{ 8}} + {{ (-5)}}}{2} \right)\implies \left(\cfrac{{{ 3}} + {{0}}}{2}\quad ,\quad \cfrac{{{ 8}} - {{ 5}}}{2} \right)[/tex]
