Question

fie punctele A(2,1),B(4,5) si C(1,-3).Aflati coordonatele punctului Dstiind ca AB=CD

Answer 1

$\overrightarrow{AB}=(x_B-x_A)\cdot\overrightarrow{i}+(y_B-y_A)\cdot\overrightarrow{j}=(4-2)\cdot\overrightarrow{i}+(5-1)\cdot\overrightarrow{j}=2\cdot\overrightarrow{i}+4\cdot\overrightarrow{j};\\\\\overrightarrow{CD}=(x_D-x_C)\cdot\overrightarrow{i}+(y_D-y_C)\cdot\overrightarrow{j}=(x_D-1)\cdot\overrightarrow{i}+[y_D-(-3)]\cdot\overrightarrow{j};\\\\x_D-1=2,\;deci\; x_D=3,\;y_D+3=4,\;deci\;y_D=1\Rightarrow D(3,1).\\\\\overrightarrow{i}\ este\ versorul\ axei\ OX,\;iar\ \overrightarrow{j}\ este\ versorul\ axei\ OY.$

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