# The vertices are (4,5),(9,10),(9,5) what are the coordinates of the the fourth vertex?

(5,10) ?

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## To find the coordinates of the fourth vertex, we need to understand the geometrical shape formed by the given vertices. It appears that the three given points are the vertices of a rectangle, with two sides parallel to the x-axis and two sides parallel to the y-axis.

To confirm this, we can calculate the distances between the given vertices. The distance between (4,5) and (9,5) is 5 units, while the distance between (4,5) and (4,10) is also 5 units. Similarly, the distance between (9,10) and (9,5) is 5 units, while the distance between (9,10) and (4,10) is also 5 units. Therefore, these measurements confirm that the shape formed by the given points is a rectangle.

Now, we can use this information to find the fourth vertex. Since the sides of the rectangle are parallel to the x-axis and y-axis, we know that the x-coordinate of the fourth vertex will be the same as the x-coordinate of the second vertex (9), and the y-coordinate will be the same as the y-coordinate of the third vertex (5). So, the coordinates of the fourth vertex are (9,5).