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The coordinates of endpoint A in AB are A(-3,0) if the midpoint of the segment is at M(2,3) what are the coordinates of point B?

Respuesta :

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -3}}\quad ,&{{ 0}})\quad % (c,d) B&({{ c}}\quad ,&{{ d}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)[/tex]

[tex]\bf midpoint\implies \left( \cfrac{c-3}{2},\cfrac{d+0}{2} \right)=(2,3)\implies \begin{cases} \cfrac{c-3}{2}=2\\\\ \cfrac{d+0}{2}=3 \end{cases} \\\\\\ \cfrac{c-3}{2}=2\implies c-3=4\implies \boxed{c=7} \\\\\\ \cfrac{d}{2}=3\implies \boxed{d=6}[/tex]

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