Question

in reperul cartezian xoy se considera punctele a(-1,3) si b(4,0) calculati coordonatele simetricului punctului b fata de punctul a

Answer 1

$\text{Fie }M(x_M, y_M)\text{ simetricul lui } B\text{ fa\c t\u a de A}\Leftrightarrow A\text{ mijloc }[BM]\Rightarrow\\\displaystyle\left \{ {{\displaystyle x_A=\frac{x_B+x_M}2} \atop {\displaystyle y_A=\frac{y_B+y_M}2}} \right. \Rightarrow \displaystyle\left \{ {{x_M=2x_A-x_B} \atop {y_M=2y_A-y_B}} \right. \Rightarrow \left \{ {{x_M=-6} \atop {y_M=6}} \\\right. \\\Rightarrow M(-6,6)$