Question

#28 please, don't understand it

Answer 1

28)

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ 1}}\quad ,&{{ 7}})\quad % (c,d) C&({{ x}}\quad ,&{{ y}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{x+1}{2}~,~\cfrac{y+7}{2} \right)=\stackrel{B}{(-3,1)}\implies \begin{cases} \cfrac{x+1}{2}=-3\\\\ x+1=-6\\ \boxed{x=-7}\\ ----------\\ \cfrac{y+7}{2}=1\\\\ y+7=2\\ \boxed{y=-5} \end{cases}$

29)

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ x}}\quad ,&{{ y}})\quad % (c,d) C&({{ -5}}\quad ,&{{ 4}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{-5+x}{2}~,~\cfrac{4+y}{2} \right)=\stackrel{B}{(-2,5)}\implies \begin{cases} \cfrac{-5+x}{2}=-2\\\\ -5+x=-4\\ \boxed{x=1}\\ -------\\ \cfrac{4+y}{2}=5\\\\ 4+y=10\\ \boxed{y=6} \end{cases}$



so.. let's also do 32)

32)

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ x}}\quad ,&{{ y}})\quad % (c,d) C&({{ \frac{5}{3}}}\quad ,&{{ -6}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)$

$\bf \left( \cfrac{\frac{5}{3}+x}{2}~,~\cfrac{-6+y}{2} \right)=\stackrel{B}{\left( \frac{8}{3},4 \right)}\implies \begin{cases} \cfrac{\frac{5}{3}+x}{2}=\cfrac{8}{3}\\\\ \frac{5}{3}+x=\frac{16}{3}\\ x=\frac{16}{3}-\frac{5}{3}\\\\ \boxed{x=\frac{11}{3}}\\ ------\\ \cfrac{-6+y}{2}=4\\\\ -6+y=8\\ \boxed{y=14} \end{cases}$