Question

If two vertices of an equilateral triangle have integral

coordinates then the third vertex will have

• A. Integral coordinates
• B. Rational coordinates
• C. At least one irrational coordinate
• D. Irrational coordinates

Answer 1

Answer: (C)

At least one irrational coordinate

Answer 2

If (x₁, y₁) and (x₂,y₂) are two vertices of an equilateral triangle have integral co-ordinate then third vertex will be

$\left( \frac{(x_{1} + x_{2}) \pm (y_{1} - y_{2})\sqrt{3}}{2},\frac{(y_{1} + y_{2}) \mp \sqrt{3}(x_{1} - x_{2})}{2} \right)$

Irrational co-ordinates.