a) check the picture below
b)
hmm where is that point A anyway? sounds like it's asking the same thing as in part a)
c)
well, where's M, the midpoint of BC, let's check.
[tex]\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
B&({{ 1}}\quad ,&{{ 4}})\quad
% (c,d)
C&({{ 9}}\quad ,&{{ 10}})
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
M=\left( \cfrac{9+1}{2}~,~\cfrac{10+4}{2} \right)\implies M=(5,7)[/tex]
now, the coordinator says that the midpoint of MC is at 6,8, let's check.
[tex]\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
M&({{ 5}}\quad ,&{{ 7}})\quad
% (c,d)
C&({{ 9}}\quad ,&{{ 10}})
\end{array}\qquad
% coordinates of midpoint
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
N=\left( \cfrac{9+5}{2}~,~\cfrac{10+7}{2} \right)\implies N=\left(7~,~\frac{17}{2} \right)\implies N=\left(7~,~8\frac{1}{2} \right)[/tex]
