Question

On a Cartesian coordinate plane, points $(2,1)$ and $(3, 4)$ are adjacent points on a square. What is the area of the square?

Answer 1

10

Explanation:

We use the distance formula to find the distance between the two points, which is the side length of the square.. Therefore, the area of the square is 10.

Answer 2

Hey there! :)

Answer:

A = 10 units².

Explanation:

To solve this, we need to find the distance between the two points to derive the side-lengths of the square. Use the distance formula:

`d = √((x_2 - x_1)^2 + (y_2-y_1)^2)`

Plug in points into the formula to find the distance:

`d = √((3 - 2)^2 + (4-1)^2)`

Simplify:

`d = √((1)^2 + (3)^2)`

`d = √((1) + (9))`

`d = √(10)`

Find the area of the square using the formula A = s² where s = √10:

A = (√10)²

A = 10 units².