We discovered that to find the coordinate patterns, we needed to write down the coordinates of x and y into a table. We did this and then found the difference between each number. For x we found that the difference was +3 but started at 2 therefore the formula for x is 3n-1. For y we found that the pattern was +1 which means the formula for y is n+1.
Following the coordinate problems we thought we should prove that the midpoint equations would be correct by finding the formula for the diagonals. We started off by finding the co-ordinates of the two diagonals, for example, on the bottom line (which we named a) we had the co-oridnates of 1,0. On the upper line (named b), we had the co-ordinates of 3,4. We then used the formula of x1 + x2 divided by 2, gave the x co-ordinate (1+3 divided by 2). Then we did the second numbers so y1 + y2 divided by 2 (0+4 divided by 2) gave the y co-ordinate. In conclusion, we ended up with the co-ordinates 2,2 which gave the midpoint of the first square, proving that it was correct.