If all the vertices of a triangle have integral coordinates, then the triangle may be (a) right-angle (b) equilateral (c) isosceles (d) none of these

Options

A. right-angled
B. equilateral
C. isoosceles
D. none of these

Answer

B

Explanation

Let `(x_(1),y_(1)) B(x_(2),y_(2)) and C(x_(3),y_(3))` be the vertices of a `Delta ABC` such that `x_(1) s and y_(1)` are integers. Then ,
`Delta " Area of" Delta ABC` = a rational numbers
`Delta=(sqrt(3))/(4)("side")^(2)=(sqrt(3))/(4)xx` an integer =a rational numbers
So, the triangle cannot be equilateral.