In a plane there are two families of lines `y=x+r, y=-x+r`, where `r in {0, 1, 2, 3, 4 }`. The number of squares of diagonals of length 2 formed by the lines is:

Explanation

To solve the problem, we need to determine how many squares of diagonals of length 2 can be formed by the given families of lines. The lines are defined as \( y = x + r \) and \( y = -x + r \) for \( r \) in the set \{0, 1, 2, 3, 4\}.

### Step-by-Step Solution:

1. **Understanding the Lines**:
- The lines \( y = x + r \) are diagonal lines with a positive slope, while the lines \( y = -x + r \) are diagonal lines with a negative slope.
- For each value of \( r \), there are two lines: one from the first family and one from the second family.

2. **Finding the Slope Intersections**:
- The lines will intersect at points that can potentially be the vertices of squares.
- For each \( r \), the lines will intersect at the points:
- \( (r, 0) \) for \( y = x + r \)
- \( (0, r) \) for \( y = -x + r \)

3. **Length of the Diagonal**:
- The length of the diagonal of a square is given as 2 units.
- The relationship between the side length \( s \) of a square and its diagonal \( d \) is given by the formula:
\[ d = s\sqrt{2} \]
- Therefore, if \( d = 2 \), we can find \( s \):
\[ 2 = s\sqrt{2} \implies s = \frac{2}{\sqrt{2}} = \sqrt{2} \]

4. **Counting the Squares**:
- To form a square, we need two pairs of parallel lines.
- For each \( r \), we can choose two lines from the first family and two lines from the second family.
- Since \( r \) can take on 5 values (0, 1, 2, 3, 4), we can choose 2 lines from the 5 available lines in each family.

5. **Calculating the Combinations**:
- The number of ways to choose 2 lines from 5 is given by the combination formula:
\[ \binom{n}{k} = \frac{n!}{k!(n-k)!} \]
- Thus, the number of ways to choose 2 lines from the first family is \( \binom{5}{2} \) and from the second family is also \( \binom{5}{2} \).
- Therefore, the total number of squares formed is:
\[ \text{Total Squares} = \binom{5}{2} \times \binom{5}{2} = 10 \times 10 = 100 \]

### Final Answer:
The number of squares of diagonals of length 2 formed by the lines is **100**.