Answer :
Formula used:
(0, –1), (2, 1), (0, 3) and (–2, 1)
Let the vertices be taken as A (0, –1), B (2, 1), C (0, 3) and D (–2, 1).
Distance of AB
⇒ AB = √ ((2 – 0)2 + ((1 – (–1))2)
⇒ AB = √ ((2 – 0))2 + (1 + 1)2)
⇒ AB = √ ((2)2 + (2)2)
⇒ AB = √ (4 + 4)
⇒ AB = √ 8
Distance of BC
⇒ BC= √ ((0 – 2)2 + (3 – 1)2)
⇒ BC = √ ((–2)2 + (2)2)
⇒ BC = √ (4 + 4)
⇒ BC = √ 8
Distance of CD
⇒ CD = √ ((–2 – 0)2 + (1 – 3)2)
⇒ CD = √ ((–2)2 + (–2)2)
⇒ CD = √ (4 + 4)
⇒ CD = √8
Distance of AD
⇒ AD = √ ((–2 – 0)2 + (1 – (–1))2)
⇒ AD = √ ((–2 – 0)2 + (1 + 1)2)
⇒ AD = √ ((–2)2 + (2)2)
⇒ AD = √ (4 + 4)
⇒ AD = √ 8
Distance of AC
⇒ AC = √ ((0 – 0)2 + (3 – (–1))2)
⇒ AC = √ ((0 – 0)2 + (3 + 1)2)
⇒ AC = √ ((0)2 + (4)2)
⇒ AC = √ (0 + 16)
⇒ AC = √ 16
⇒ AC = 4
Distance of BD
⇒ AC = √ ((–2 – 2)2 + (1 – 1)2)
⇒ AC = √ ((–4)2 + (0)2)
⇒ AC = √ (16 + 0)
⇒ AC = √ 16
⇒ AC = 4
AB = BC = CD = DA = √8 (That is, all the sides are equal.)
AC = BD = 4. (That is, the diagonals are equal.)
Hence the points A, B, C and D form a square.
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