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प्रश्न
Prove that the points (1 , 1) , (-1 , -1) and (`- sqrt 3 , sqrt 3`) are the vertices of an equilateral triangle.
उत्तर
PQ = `sqrt ((1 + sqrt 3)^2 + (1 - sqrt 3)^2) = sqrt (4 + 4) sqrt 8` units
QR = `sqrt ((-sqrt 3 + 1)^2 + (sqrt 3 + 1)^2) = sqrt (4 + 4) = sqrt 8` units
PR = `sqrt ((- 1 + 1)^2 + (-1 + 1)^2) = sqrt (4 + 4) = sqrt 8` units
∵ PQ = QR = PR
∴ PQR is an equilateral triangle.
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