Question

The area of a square is 41 square units. Two of its vertices are located at (0, -3) and (4,2).

Select all points that could be a third vertex of this'square.

A. (0,7)
B. (-5,1)
C. (5.-7)
D. (9.-2)
E. (4.-6)

Answer 1

To find the third vertex of the square, we can use the fact that the opposite sides of a square are parallel and equal in length. By calculating the distance between the given vertices, we can determine which of the given points could be the third vertex of the square.

Step-by-step explanation:

To find the third vertex of the square, we can use the fact that the opposite sides of a square are parallel and equal in length. So, if we know two vertices of the square, we can find the length of one side and then find the coordinates of the remaining two vertices.

From the given information, we know that the distance between (0, -3) and (4, 2) is the length of one side of the square. Using the distance formula, we can calculate this distance to be √((4 - 0)^2 + (2 - (-3))^2) = 5 units.

Now, for a point to be a vertex of the square, it should be 5 units away from each of the given vertices. We can calculate the distance between each of the remaining points and the given vertices to determine which ones could be the third vertex of the square.

Using this approach, we find that points A. (0, 7) and E. (4, -6) could be the third vertex of the square. Therefore, the correct options are A and E.