https://file.aiquickdraw.com/mathbot/file/1737293790185pb45oygn.jpg

The image shows a parallelogram ABCD on a coordinate plane with the points labeled as follows:

- Point A (-11, 23)
- Point B (-13, 29)
- Point C (5, 22)

You are asked to find the coordinates of point D.

### Solution:
In a parallelogram, opposite sides are parallel and equal in length. Thus, the vector from A to B is equal to the vector from D to C. We can find the coordinates of point D by using this property.

The vector from A to B is:
\[
\overrightarrow{AB} = B - A = (-13 - (-11), 29 - 23) = (-2, 6)
\]

Since \(\overrightarrow{AB} = \overrightarrow{DC}\), the vector from D to C must also be (-2, 6). Therefore, to find D, we can apply the vector to point C:
\[
D = C - \overrightarrow{AB} = (5, 22) - (-2, 6) = (5 + 2, 22 - 6) = (7, 16)
\]

Thus, the coordinates of point D are (7, 16).

Let me know if you need further clarification or details! Also, here are a few related questions:

1. What is the general formula for finding the coordinates of a point in a parallelogram?
2. How do you find the area of a parallelogram given its vertex coordinates?
3. What is the distance between two points in a coordinate plane?
4. How do you determine if a quadrilateral is a parallelogram from its vertex coordinates?
5. How can you prove that opposite sides of a parallelogram are parallel using vectors?

**Tip:** When dealing with parallelograms, always remember that opposite sides are not only parallel but also equal in length. This can help simplify many problems like this one.

ABCD is a parallelogram. What are the coordinates of point D? Given points are A(-11, 23), B(-13, 29), and C(5, 22).

Learn how to calculate the coordinates of a missing point in a parallelogram using vector properties. This solution involves understanding coordinate geometry, the vector addition formula, and the properties of parallelograms. Example: Find the coordinates of D given A(-11, 23), B(-13, 29), and C(5, 22).

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