The coordinates of two consecutive vertices `A` and ` B` of a regular hexagon `A B C D E F` are `(1,0)` and `(2,0),` respectively. The equation of the diagonal `C E` is

The vertices of the rectangle ABCD are A(-1,0), B(2, 0), C(a, b) and D(-1, 4). Then the length of the diagonal AC is

If in parallelogram ABDC , the coordinate of A , B and C are respectively (1,2) , (3,4) and (2,5) , then the equation of the diagonal AD is

If the coordinates of the points A,B,C be (-1,5),(0,0) and (2,2) respectively, and D be the middle point of BC , then the equation of the perpendicular drawn from B to the line AD is

A,B, and C are vertice of DeltaABC,D,E and F are mid point of side AB,BC and AC respectively. If the coordinates of A, D and F are (-3,5),(5,1) and (-5,-1) respectively. Find the coordinates of B,C and E.

Let A,B,C be angles of triangles with vertex A -= (4,-1) and internal angular bisectors of angles B and C be x - 1 = 0 and x - y - 1 = 0 respectively. If A,B,C are angles of triangle at vertices A,B,C respectively then cot ((B)/(2))cot .((C)/(2)) =

a and b form the consecutive sides of a regular hexagon A B C D E Fdot Column I, Column II If vec C D=x vec a+y vec b , then, p. x=-2 If vec C E=x vec a+y vec b , then, q. x=-1 If vec A E=x vec a+y vec b , then, r. y=1 vec A D=-x vec b , then, s. y=2

A regular polygon has two of its consecutive diagonals as the lines sqrt(3)x+y-sqrt(3) and 2y=sqrt(3) . Point (1,c) is one of its vertices. Find the equation of the sides of the polygon and also find the coordinates of the vertices.

If the roots of the equation x^(2)-bx+c=0 are two consecutive integers, then b^(2)-4c is

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is (a) 1/2 (b) 1/5 (c) 1/10 (d) 1/20

Let A, B, C, D, E represent vertices of a regular pentagon ABCDE. Given the position vector of these vertices be veca, veca + vecb, vecb, lamda veca and lamda vecb , respectively. The ratio (AD)/(BC) is equal to