The points $Q(1,-1), R(-1,0)$ and $S(0,1)$ are three vertices of a parallelogram. The coordinates of the fourth vertex of the parallelogram could be
(A) $(-2,2)$
(B) $(0,-1)$
(C) $(0,0)$
(D) $\left(\frac{3}{2}, \frac{1}{2}\right)$
(E) $(-1,1)$
We plot the first three vertices on a graph.

We see that one possible location for the fourth vertex, $V$, is in the second quadrant:

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-144.jpg?height=515&width=616&top_left_y=2109&top_left_x=814)

If $V S Q R$ is a parallelogram, then $S V$ is parallel and equal to $Q R$.

To get from $Q$ to $R$, we go left 2 units and up 1 unit.

Therefore, to get from $S$ to $V$, we also go left 2 units and up 1 unit.

Since the coordinates of $S$ are $(0,1)$, then the coordinates of $V$ are $(0-2,1+1)=(-2,2)$.

This is choice (A).

There are two other possible locations for the fourth vertex, which we can find in a similar way. These are $U(0,-2)$ and $W(2,0)$.

Using these points, we can see that $S Q U R$ and $S W Q R$ are parallelograms. But $(0,-2)$ and $(2,0)$ are not among the possible answers.

Therefore, of the given choices, the only one that completes a parallelogram is $(-2,2)$.

ANSWER: (A)