Question

The coordinates of three vertices of a square are (3, 2), (-1, 2), and (-1, -2). What are the coordinates of the fourth vertex?

A)4,5
B)2,3
C)1,2
D)3,2

Answer 1

To find the coordinates of the fourth vertex of a square given three vertices, determine the side length and use it to determine the location of the missing vertex by following the square's properties. The coordinates of the missing vertex in this case are (3, -2).

Step-by-step explanation:

The coordinates of three vertices of a square are (3, 2), (-1, 2), and (-1, -2). Since a square has all sides of equal length and the sides are parallel to the coordinate axes, we can find the length of one side by calculating the distance between two adjacent vertices. For instance, the distance between (3, 2) and (-1, 2) is 4 units (because they lie on the same horizontal line and we can just subtract the x-coordinates). Since this is the length of one side of the square, we can find the coordinates of the fourth vertex by moving 4 units in the positive x direction from the vertex (-1, -2). Thus, the fourth vertex will have an x-coordinate of -1 + 4 = 3. The y-coordinate of the fourth vertex will be the same as that of the vertex (-1, -2), which is -2. Therefore, the coordinates of the fourth vertex are (3, -2).