On a Cartesian coordinate plane, points $(2,1)$ and $(3, 4)$ are adjacent points on a square. What is the area of the square?
We use the distance formula to find the distance between the two points, which is the side length of the square.
$\sqrt{(3-2)^2+(4-1)^2}=\sqrt{1+9} = \sqrt{10}$. Therefore, the area of the square is $(\sqrt{10})^2 = \boxed{10}$.
10
Level 3
Algebra
Problem: On a Cartesian coordinate plane, points $(2,1)$ and $(3, 4)$ are adjacent points on a square. What is the area of the square?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the area of the square, first determine the distance between the points (2,1) and (3,4). This distance represents the length of one side of the square. Use the distance formula: 

Distance = √[(x2 - x1)² + (y2 - y1)²]. 

Substituting the coordinates, we have:

Distance = √[(3 - 2)² + (4 - 1)²] = √[1² + 3²] = √[1 + 9] = √10.

Since the points are adjacent vertices of the square, the length of one side of the square is √10. 

The area of a square is calculated as the side length squared. Therefore, the area is:

Area = (side length)² = (√10)² = 10.

Thus, the final answer is 10.<|END_OF_LATENT|> The final answer is $10$.