Examine the vertices (-1, 2), (3, 2), (1, 0), (1, 4) are belong to square. If yes find the area of a square.
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We are going to find distance between sides
AB= (5−1) 2 +(4−2) 2 = 16+4 = 20 =2 ROOT 5
BC= (3−5) 2 +(8−4) 2 = 4+16 = 20 =2 ROOT 5
CD= (−1−3) 2 +(6−8) 2 = 16+4 = 20 =2 ROOT 5
DA= (1+1) 2 +(2−6) 2 = 4+16 = 20 =2 ROOT 5
∴ AB=BC=CD=DA
Now, we are going to find distance between diagonals.
AC= (3−1) 2 +(6−2) 2 = 4+16 = 20 =2 ROOT 5
BD= (−1+5) 2 +(6−4) 2 = 16+4 = 20 =2 ROOT 5
∴ AC=BD
So, here we can see distance between all sides and diagonals are equal.
∴ Points A,B,C and D are the vertices of a square.
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