Let (2, 1), (- 3, -2) and (a, b) form a triangle. Show that the collection of the points (a, b) forms a line for which triangle is isosceles. Find the equation of the line.

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

If the area of the triangle formed by the points (2a,b), (a+b, 2b+a) and (2b, 2a) be Delta_(1) and the area of the triangle whose vertices are (a+b, a-b), (3b-a, b+3a) and (3a-b, 3b-a) be Delta_(2) , then the value of Delta_(2)//Delta_(1) is

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, -1), (2, 1) and (0, 3). Find the ratio of the area of the triangle formed to the area of the given triangle

Show that the points : A (0,1,2),B(2,-1,3) and C (1,-3,1) are vertices of an isosceles right angle triangle.

If the points A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) are collinear, then area of triangle ABC is:

Find the area of the triangle formed by joining the mid points of the sides of the triangle whose vertices are (0,-1), (2,1) and (0,3). Find the ratio of the area of the triangle formed to the area of the given triangle.

The vertices of a triangle are (4, -3), (-2, 1) and (2, 3). Find the co-ordinates of the circumcentre of the triangle. [Circumcentre is the point of concurrence of the right-bisectors of the sides of a triangle.]

Consider A(2,3,4),B(4,3,2) and C(5,2,-1) be any three points. Find the area of triangle ABC.

Let cosA+cosB + cos C=3/2 in a triangle then the type of the triangle is