Prove that all the vertices of an equilateral triangle can not be integral points (an integral point is a point both of whose coordinates are integers).

Prove that the coordinates of the vertices of an equilateral triangle can not all be rational.

A point both of whose coodinate are negative will be in

The number of integral point inside the triangle made by the line 3x + 4y - 12 =0 with the coordinate axes which are equidistant from at least two sides is/are : ( an integral point is a point both of whose coordinates are integers. )

If two vertices of an equilaterla triangle have integral coordinates, then the third vetex will have

Let C be any circle with centre (0,sqrt(2))dot Prove that at most two rational points can be there on Cdot (A rational point is a point both of whose coordinates are rational numbers)

Let C be any circle with centre (0,sqrt(2))dot Prove that at most two rational points can be there on Cdot (A rational point is a point both of whose coordinates are rational numbers)

The number of integral points on the hyperbola x^2-y^2= (2000)^2 is (an integral point is a point both of whose co-ordinates are integer) (A) 98 (B) 96 (C) 48 (D) 24

The number of integral points on the hyperbola x^2-y^2= (2000)^2 is (an integral point is a point both of whose co-ordinates are integer) (A) 98 (B) 96 (C) 48 (D) 24

Number of shortest ways in which we can reach from the point (0, 0, 0) to point (3.7, 11) in space where the movement is possible only along the x-axis, y axis and z-axis or parallel to them and change of axes is permitted only at integral points (an integral point is one which has its coordinate as integer) is

Find the coordinates of the vertices of an equilateral triangle of side 2a as shown in Figure.