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Question
Show that the points A (5, 6), B (1, 5), C (2, 1) and D (6, 2) are the vertices of a square ABCD.
Solution
AB = `sqrt((1 - 5)^2 + (5 - 6)^2) = sqrt(16 +1) = sqrt(17)`
BC = `sqrt((2 - 1)^2 + (1 - 5)^2) = sqrt(1+16) = sqrt(17)`
CD = = `sqrt((6 - 2)^2 + (2 - 1)^2) = sqrt(16 + 1) = sqrt(17)`
DA = = `sqrt((5 - 6)^2 + (6 - 2)^2) = sqrt(1+16) = sqrt(17)`
AC = = `sqrt((2 - 5)^2 + (1 - 6)^2) = sqrt(9+25) = sqrt(34)`
BD = = `sqrt((6 - 1)^2 + (2 - 5)^2) = sqrt(25+9) = sqrt(34)`
Since, AB = BC = CD = DA and AC = BD,
A, B, C and D are the vertices of a square.
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