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If the three consecutive vertices of a parallelogram are $(-2,-1),(1,0)$ and $(4,3)$, then what are the coordinates of the fourth vertex?
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Verified Answer
The correct answer is:
$(1,2)$
Given vertices of parallelogram are $(-2,-1),(1,0),(4,3)$
Let the fourth vertex be $(\mathrm{x}, \mathrm{y})$ We know, in a parallelogram diagonals bisect each other.
i.e, Midpoint of $\mathrm{AC}=$ Midpoint of $\mathrm{BD}$ $\Rightarrow\left(\frac{-2+4}{2}, \frac{-1+3}{2}\right)=\left(\frac{\mathrm{X}+1}{2}, \frac{\mathrm{Y}+0}{2}\right)$
$\Rightarrow(1,1)=\left(\frac{\mathrm{X}+1}{2}, \frac{\mathrm{Y}+0}{2}\right)$
$\Rightarrow \mathrm{X}+1=2 ; \mathrm{Y}+0=2$
$\Rightarrow \mathrm{X}=1, \mathrm{Y}=2$
Let the fourth vertex be $(\mathrm{x}, \mathrm{y})$ We know, in a parallelogram diagonals bisect each other.
i.e, Midpoint of $\mathrm{AC}=$ Midpoint of $\mathrm{BD}$ $\Rightarrow\left(\frac{-2+4}{2}, \frac{-1+3}{2}\right)=\left(\frac{\mathrm{X}+1}{2}, \frac{\mathrm{Y}+0}{2}\right)$
$\Rightarrow(1,1)=\left(\frac{\mathrm{X}+1}{2}, \frac{\mathrm{Y}+0}{2}\right)$
$\Rightarrow \mathrm{X}+1=2 ; \mathrm{Y}+0=2$
$\Rightarrow \mathrm{X}=1, \mathrm{Y}=2$
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