Question

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?

Answer 1

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.