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Q.
The points $(-1, 0)$ and $(-2, 1)$ are the two extremities of a diagonal of a parallelogram. If $(-6, 5)$ is the third vertex, then the fourth vertex of the parallelogram is
Let the points of parallelogram are $A(-2,1), B(-6,5)$, $C(-1,0)$ and $D(x, y)$
We know that, diagonals of parallelogram bisect each other.
$\left(\frac{-2-1}{2}, \frac{1+0}{2}\right)=\left(\frac{x-6}{2}, \frac{y+5}{2}\right)$
$\Rightarrow \frac{-3}{2}=\frac{x-6}{2}$ and $\frac{1}{2}=\frac{y+5}{2}$
$\Rightarrow -3=x-6$ and $1=y+5$
$\Rightarrow x=-3+6$ and $y=1-5$
$\Rightarrow x=3$ and $y=-4$
Thus, coordinates of fourth vertex of paralleogram are $(3,-4)$
