# What is the side length of a square if A (4, 1) AND C (8, 5) are opposite vertices?

October 9, 2021 | education

| The opposite vertices are connected by the diagonal of the square d. Its size is related to the size of the side and the ratio:

d ^ 2 = a ^ 2 + a ^ 2 = 2a ^ 2;

a = √ (d ^ 2/2) = d / √2.

Find the length of the diagonal as the distance between points A and C:

d = √ ((XC – XA) ^ 2 + (YC – YA)) = √ (8 – 4) ^ 2 + (5 – 1) ^ 2 = √ (16 + 16) = 4√2;

a = (4√2) / √2 = 4.

Answer: 4.

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