Grayson is designing a rectangular athletic field. On his scale drawing, the vertices of the rectangle are (4, 5), (9, 10), and (9, 5). What are the coordinates of the fourth vertex?

The coordinates of the fourth vertex are (4, 10). It is observed that there is a pair of vertices with the same coordinate. This is the y coordinate 5, hence we can assume that the missing vertex is paired with (9, 10). We can infer from this that the missing y coordinate is 10. For the x coordinate, it can also be seen as pairs. Two vertices have the x coordinate 9, so we can deduce that the fourth vertex has an x coordinate 4.