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These coordinates (-2,4) , (3,4) and (3, -1)

which graphed coordinates will represent three vertices of a square.
A. (-2, -1)
B. (-2,-4)
C. (-1,-2)
D. (2, -1)

1 answer

To determine which of the given options will complete a square using the vertices (-2, 4), (3, 4), and (3, -1), we can analyze the coordinates.

  1. Identifying the given points:

    • A = (-2, 4)
    • B = (3, 4)
    • C = (3, -1)

  2. Understanding the shape:

    • The segment AB is horizontal (same y-coordinate) from (-2, 4) to (3, 4).
    • The segment BC is vertical (same x-coordinate) from (3, 4) down to (3, -1).

  3. Calculating the missing vertex:

    • To form a square, we need one more vertex:
      • Vertical distance between points B and C is 5 units (from 4 to -1).
      • Therefore, the distance from A should also be 5 units vertically down from point A, giving us the missing vertex’s coordinates.

  4. Calculating from A:

    • A: (-2, 4)
    • Move vertically down by 5 units to find the fourth vertex: \[ (-2, 4 - 5) = (-2, -1) \]

  5. Identifying the correct answer:

    • The potential candidate from the options that matches calculated coordinates (-2, -1) is A.

So, the correct option that will represent the fourth vertex of the square is A. (-2, -1).