A square graphed on the coordinate plane has a diagonal with endpoints E (2,3) and F (0,-3) what are the coordinates of the endpoints of the other diagonal?

To find the endpoints of the other diagonal of the square, we need to determine the location of the other two vertices of the square. Since the square is symmetric, we can find the vertices by reflecting the given endpoints (E and F) across the midpoint of the given diagonal.

Step 1: Find the midpoint of the given diagonal
To find the midpoint of the given diagonal, we can use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Let's substitute the given coordinates into the formula:
Midpoint = ((2 + 0)/2, (3 + (-3))/2)
Midpoint = (1, 0)

So, the midpoint of the given diagonal is (1, 0).

Step 2: Reflect the given endpoints across the midpoint
To reflect a point across a line, we need to consider the difference between the coordinates of the point and the midpoint, and then subtract this difference from the midpoint.

Let's find the reflection of point E:
Difference in x-coordinates = 2 - 1 = 1
Difference in y-coordinates = 3 - 0 = 3

Reflection of E = (1 - 1, 0 - 3) = (0, -3)

Now let's find the reflection of point F:
Difference in x-coordinates = 0 - 1 = -1
Difference in y-coordinates = -3 - 0 = -3

Reflection of F = (1 - (-1), 0 - (-3)) = (2, 3)

So, the coordinates of the endpoints of the other diagonal are (0, -3) and (2, 3).