Connor is constructing parallelogram ABCD . He has plotted A at $$ (-2,4), \mathrm{B} $$ at $$ (0,3) $$, and D at $$ (-3,2) $$. Which coordinate could be the location of point C $$ \mathrm{OC}(0,0) $$

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To find the coordinates of point $$ C $$ in parallelogram $$ ABCD $$, we can use the property that the diagonals of a parallelogram bisect each other. This means that the midpoint of diagonal $$ AC $$ should be the same as the midpoint of diagonal $$ BD $$.

Let's denote the coordinates of the points as follows:
- $$ A(-2, 4) $$
- $$ B(0, 3) $$
- $$ D(-3, 2) $$
- $$ C(x, y) $$ (unknown coordinates)

### Step 1: Calculate the midpoint of diagonal $$ BD $$

The midpoint $$ M_{BD} $$ of points $$ B $$ and $$ D $$ can be calculated using the midpoint formula:
$$
M_{BD} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
$$
Substituting the coordinates of $$ B $$ and $$ D $$:
$$
M_{BD} = \left( \frac{0 + (-3)}{2}, \frac{3 + 2}{2} \right) = \left( \frac{-3}{2}, \frac{5}{2} \right)
$$

### Step 2: Calculate the midpoint of diagonal $$ AC $$

The midpoint $$ M_{AC} $$ of points $$ A $$ and $$ C $$ is given by:
$$
M_{AC} = \left( \frac{-2 + x}{2}, \frac{4 + y}{2} \right)
$$

### Step 3: Set the midpoints equal to each other

Since $$ M_{AC} = M_{BD} $$, we can set the coordinates equal:
1. For the x-coordinates:
$$
\frac{-2 + x}{2} = \frac{-3}{2}
$$
2. For the y-coordinates:
$$
\frac{4 + y}{2} = \frac{5}{2}
$$

### Step 4: Solve for $$ x $$ and $$ y $$

**For the x-coordinate:**
$$
-2 + x = -3 \implies x = -3 + 2 \implies x = -1
$$

**For the y-coordinate:**
$$
4 + y = 5 \implies y = 5 - 4 \implies y = 1
$$

### Conclusion

The coordinates of point $$ C $$ are $$ (-1, 1) $$.

Thus, the location of point $$ C $$ is $$ (-1, 1) $$. The coordinate $$ (0, 0) $$ is not a valid location for point $$ C $$.
The coordinates of point $$ C $$ are $$ (-1, 1) $$.

Connor is constructing parallelogram ABCD . He has plotted A at \( (-2,4), \mathrm{B} \) at \( (0,3) \), and D at \( (-3,2) \). Which coordinate could be the location of point C \( \mathrm{OC}(0,0) \)

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