How many squares in a 2x3 plane have two or more vertices on dots in a grid? All dots are an equal distance from their nearest neighbors.

i got 15

31 To find the number of squares in a 2x3 plane that have two or more vertices on dots in a grid, we can break it down step by step.

Step 1: Understand the grid
In a 2x3 grid, we have 2 rows and 3 columns, resulting in a total of 6 dots.

Step 2: Identify the squares
A square is formed when its four vertices (corners) are dots on the grid. We want to find the number of squares where two or more of these vertices lie on the dots of the grid.

Step 3: Count the squares
We'll start by counting the squares that have all four corners on the dots:

- There are two squares formed by the four corners of the grid, one in the top left and one in the bottom right.
- Additionally, we can form a square using any four adjacent dots on one side of the grid. For example, we can form a square using the top left corner, the dot to its right, the dot below it, and the dot diagonally below and to the right. By applying this approach, we can find a total of four squares.

So, in total, there are six squares (2 + 4) in a 2x3 plane that have two or more vertices on dots in the grid.