Final answer:
To find the other vertex of the square, calculate the distance between two points and use the characteristics of a square.
Step-by-step explanation:
To find the other vertex of the square, we need to understand the characteristics of a square. A square has four equal sides and four right angles. Given the three vertices (3,3), (3,3), and (3,-2), we can see that the point (3,3) is repeated twice. Since the sides of the square are equal, we can find the length of one side by calculating the distance between any two points.
The distance formula is: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula between (3,3) and (3,-2), we get d = sqrt((3-3)^2 + (3-(-2))^2) = sqrt(0 + 25) = 5.
Now, we need to find the fourth vertex. Since the square's sides are equal, we can move 5 units in the vertical direction from (3,-2) to find the fourth vertex. Hence, the other vertex of the square is (3,2) (option c).
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