It seems like you're looking for pairs of values that represent the side length \( s \) and the area \( A \) of a square. The area of a square is calculated using the formula:
\[ A = s^2 \]
Let's analyze the sets of points you provided:
-
(1,1), (2,4), (3,9)
- For \( s = 1 \), \( A = 1^2 = 1 \)
- For \( s = 2 \), \( A = 2^2 = 4 \)
- For \( s = 3 \), \( A = 3^2 = 9 \)
All these pairs are correct.
-
(1,2), (3,4), (5,6)
- For \( s = 1 \), \( A = 1^2 = 1 \) (not 2)
- For \( s = 3 \), \( A = 3^2 = 9 \) (not 4)
- For \( s = 5 \), \( A = 5^2 = 25 \) (not 6)
None of these pairs are correct according to the area formula for a square.
-
(1,2), (2,2), (3,6)
- For \( s = 1 \), \( A = 1^2 = 1 \) (not 2)
- For \( s = 2 \), \( A = 2^2 = 4 \) (not 2)
- For \( s = 3 \), \( A = 3^2 = 9 \) (not 6)
Again, none of these pairs are correct according to the area formula for a square.
In conclusion, the only valid pairs according to the area of a square are from the first set: (1,1), (2,4), (3,9).