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

Question

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

Select the point that could be a third vertex of this square.

A. (0,7)
B. (-5,1)
C.(5,13)
D.(-2,-2)
E.(4,-6)

Answer (Expert Verified)

The vertices of the square are the coordinates of the endpoints

The third vertex of the square could be (0,7) or (-5,1)

How to determine the third vertex

Two vertices of the square are:

(0,-3) and (4,2)

Calculate the distance between these vertices using:

Square both sides

The above expression represents the area of the square.

So, we have:

Next, we test the options with the given vertices (0,-3) and (4,2)

So, we have:

A. (0,7)

B. (-5,1)

C.(5,13)

D.(-2,-2)

E.(4,-6)

The vertices where at least one of the equations is true could be a third vertex of the square

Hence, a third vertex of the square could be (0,7) or (-5,1)

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