We are given that ABCD is a parallelogram, and we need to find the coordinates of point D. We have the following information:

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

To find the coordinates of point D, we can use the property of parallelograms: the diagonals bisect each other. This means the midpoint of diagonal AC is the same as the midpoint of diagonal BD.

Let's find the midpoint of diagonal AC:

$\text{Midpoint of AC} = \left( \frac{-11 + 5}{2}, \frac{23 + 22}{2} \right) = \left( \frac{-6}{2}, \frac{45}{2} \right) = (-3, 22.5)$

Now, let the coordinates of point D be $(x, y)$. Using the fact that the midpoint of BD must also be $(-3, 22.5)$, we can set up the midpoint formula for BD:

$\left( \frac{-13 + x}{2}, \frac{29 + y}{2} \right) = (-3, 22.5)$

Now, solve for $x$ and $y$:

1. $\frac{-13 + x}{2} = -3$

   Multiplying both sides by 2:

   $-13 + x = -6 \quad \Rightarrow \quad x = 7$

2. $\frac{29 + y}{2} = 22.5$

   Multiplying both sides by 2:

   $29 + y = 45 \quad \Rightarrow \quad y = 16$

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

Would you like further details, or do you have any other questions?

Here are 5 related questions to deepen your understanding:

1. How can you confirm that opposite sides of a parallelogram are parallel using vectors?
2. How can the area of parallelogram ABCD be calculated using the vertices' coordinates?
3. Can you apply this method to find a missing vertex of a trapezoid or other quadrilaterals?
4. How would you find the equation of the line passing through two points, like A and B?
5. What are some other properties of parallelograms that can help solve geometric problems?

Tip: In geometry, the midpoint formula is an essential tool for solving problems involving bisected diagonals, line segments, or centroids.