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Let's go over the problems shown in your image:

### Problem 11:
*Alexandra drew the logo shown on half-inch graph paper. Write a rule that describes the translation Alexandra used to create the shadow on the letter A.*

This question asks for a description of the translation used to form the shadow of the letter "A". To determine the correct translation, we would examine how the original letter "A" moves in relation to its shadow along the grid lines (e.g., by observing changes in coordinates or shifts along the x- and y-axes).

### Problem 12:
*Kite KLMN has vertices at K(1, 3), L(2, 4), M(3, 3), and N(2, 0). After the kite is rotated, \(K'\) has coordinates (-3, 1). Describe the rotation, and include a rule in your description. Then find the coordinates of \(L', M',\) and \(N'\).*

Here, we are given the vertices of a kite and information about the rotation of the shape. We can determine the transformation rule by identifying the center of rotation and the degree of rotation, and applying that to the other points to find the new positions of \(L', M',\) and \(N'\).

Would you like me to walk through each of these problems in more detail, starting with any particular one?

### Related Questions:
1. What is the general process for determining a translation rule on a coordinate plane?
2. How do you determine the center of rotation when given rotated coordinates?
3. What is the mathematical rule for a 90-degree rotation counterclockwise around the origin?
4. Can a reflection be mistaken for a translation or rotation? If so, how can we differentiate them?
5. How can you verify the new coordinates of a shape after applying a geometric transformation?

### Tip:
When dealing with transformations such as rotations, translations, and reflections, always check the relative distances between points and their images, as this helps clarify the nature of the transformation.

Alexandra drew the logo shown on half-inch graph paper. Write a rule that describes the translation Alexandra used to create the shadow on the letter A. Kite KLMN has vertices at K(1, 3), L(2, 4), M(3, 3), and N(2, 0). After the kite is rotated, K' has coordinates (-3, 1). Describe the rotation, and include a rule in your description. Then find the coordinates of L', M', and N'.

Solve problems involving the translation and rotation of shapes on a coordinate plane. In this example, we discuss the translation rule for a shadow and describe the rotation rule for kite KLMN, including finding the new coordinates of the vertices.

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