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If $\mathrm{A}(2,3), \mathrm{B}(1,4), \mathrm{C}(0-2)$ and $\mathrm{D}(\mathrm{x}, \mathrm{y})$ are the vertices of a
parallelogram, then what is the value of $(\mathrm{x}, \mathrm{y})$ ?
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parallelogram, then what is the value of $(\mathrm{x}, \mathrm{y})$ ?
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The correct answer is:
$(1,-3)$
As given : $\mathrm{A}(2,3), \mathrm{B}(1,4), \mathrm{C}(0,-2)$ and $\mathrm{D}(\mathrm{x}, \mathrm{y})$ are the
vertices of a parallelogram. Diagonals of a parallelogram bisect each other So, mid-point are same for both diagonals $\mathrm{AC}$ and $\mathrm{BD}$.
$\frac{2+0}{2}=\frac{1+x}{2}$ and $\frac{3-2}{2}=\frac{4+y}{2}$
$\Rightarrow \quad x=1$ and $y=-3$
$\Rightarrow \quad \mathrm{D}(\mathrm{x}, \mathrm{y})=(1,-3)$
vertices of a parallelogram. Diagonals of a parallelogram bisect each other So, mid-point are same for both diagonals $\mathrm{AC}$ and $\mathrm{BD}$.
$\frac{2+0}{2}=\frac{1+x}{2}$ and $\frac{3-2}{2}=\frac{4+y}{2}$
$\Rightarrow \quad x=1$ and $y=-3$
$\Rightarrow \quad \mathrm{D}(\mathrm{x}, \mathrm{y})=(1,-3)$
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