Question

If ABCD is a parallelogram,prove that the opposite sides are equal and the diagonals bisect each other using the position vectors of ABCD.

Answer 1

Answer on Question #81351 - Math - Geometryry

Coordinates of $B$ are equal to coordinates of $A$ plus coordinates of $v_{1}$. Coordinates of $C$ are equal to coordinates of $A$ plus coordinates of $v_{1}+v_{2}$. Coordinates of $D$ are equal to coordinates of $A$ plus coordinates of $v_{2}$. The lengths of $AB$ and $CD$ are equal to the length of $v_{1}$, the lengths of $BC$ and $AD$ are equal to the length of $v_{2}$. The coordinates of the midpoint of $AC$ are equal to the coordinates of $A$ plus coordinates of $\frac{v_{1}+v_{2}}{2}$, the coordinates of the midpoint of $BD$ are also equal to the coordinates of $A$ plus coordinates of $\frac{v_{1}+v_{2}}{2}$.

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