The image shows a math problem in German. Here's the translated version of the problem:

Draw the points

• A (2|1),
• B (2|3),
• and C (-4|3) in a coordinate system.

Tasks:

1. (a) Add a point D so that the quadrilateral ABCD is a rectangle. Provide the coordinates of point D.
2. (b) Draw the diagonals AC and BD. Provide the coordinates of the intersection point P of the diagonals.
3. (c) Reflect point A over the y-axis. Provide the coordinates of the reflected point.

Let me walk you through solving the problem:

Part (a):

We need to determine the coordinates of point D to make ABCD a rectangle. Points A, B, and C are given as:

• $A(2, 1)$
• $B(2, 3)$
• $C(-4, 3)$

To form a rectangle, the opposite sides must be parallel and of equal length. Therefore, point D must be at $(-4, 1)$, as it ensures that $AB \parallel CD$ and $AD \parallel BC$, creating a rectangle.

So, the coordinates of point D are:
D (-4, 1)

Part (b):

The diagonals of a rectangle intersect at their midpoints. The diagonals here are $AC$ and $BD$.

• Diagonal $AC$ connects $A(2,1)$ and $C(-4,3)$.
• Diagonal $BD$ connects $B(2,3)$ and $D(-4,1)$.

To find the intersection point, we calculate the midpoint of either diagonal:

• Midpoint formula:
  $\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$
• Using points $A(2, 1)$ and $C(-4, 3)$: $P = \left( \frac{2 + (-4)}{2}, \frac{1 + 3}{2} \right) = (-1, 2)$

So, the intersection point $P$ of the diagonals is:
P (-1, 2)

Part (c):

To reflect point A over the y-axis, we change the sign of the x-coordinate of point A:

• Point $A(2, 1)$ becomes $A'(-2, 1)$ after reflection.

Thus, the coordinates of the reflected point are:
A' (-2, 1)

Would you like any additional details or clarifications on the solution? Here are five related questions for further practice:

1. How do you find the slope of a line between two points?
2. What is the formula for calculating the distance between two points?
3. How would you determine if a given quadrilateral is a square instead of a rectangle?
4. How can you reflect a point over the x-axis?
5. How do you find the equation of a line through two given points?

Tip: For any rectangle, the diagonals are always equal in length and bisect each other at their midpoint.