The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie on the line y=2x+c. Find c and the remaining vertices.

The points (3,2),(0,5),(-3,2) and (0,-1) are vertices of:

A(1,3)and C(7,5) are two opposite vertices of a square. The equation of a side through A is

The points A(x,y), B(y, z) and C(z,x) represents the vertices of a right angled triangle, if

If A (2, -3) and B (-2, 1) are two vertices of a triangle and third vertex moves on the line 2x + 3y = 9, then the locus of the centroid of the triangle is :

A rectangle has opposite vertices at the points (1,2) and (5, 5). If the other vertices lie on the line x=3, find the equation of the sides of the rectangle.

If A(-1, 6), B(-3, -9) and C(5, -8) are the vertices of a triangle ABC , find the equations of its medians.

Prove that the points A (1,2,3), B(2,3,1) and C(3,1,2) are the vertices of an equilateral triangle.

Show that four points (0,-1),(6,7),(-2,3)a n d(8,3) are the vertices of a rectangle. Also, find its area.

The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices of a parallelogram ABCD. Find the vector equations of side AB and BC and also find the coordinates of point D .