A(-3,2),B(3,2) and C(-3,-2) are the vertices of the right trinagle ,right angled at A. Show that the mid point of the hypotenus is equidistant form the vertices.

The points A(-5,4), B(-1,-2) and C(5,2) are the vertices of an isosceles right angled trinagle where the right angle is at B. Find the corrdinates of D so that ABCD is a square .

ABC is a right triangle , right angled at A and D is the mid point of AB . Prove that BC^(2) =CD^2 +3BD^(2) .

If A(0,1,1), B(3, 1,5) and C(0, 3, 3) are three points show that DeltaABC is right angled at C.

A(-3, 0), B(10, -2) and C(12, 3) are the vertices of triangleABC . Find the equation of the altitude through A and B.

Statement 1 : Let the vertices of a A B C be A(-5,-2),B(7,6), and C(5,-4) . Then the coordinates of the circumcenter are (1,2)dot Statement 2 : In a right-angled triangle, the midpoint of the hypotenuse is the circumcenter of the triangle.

A (2, 5), B (-1, 3) and C (5, -1) are the vertices of a triangle. The image of the point (1,2) with respect to the median through A is

A(-3,0),B(1,3),C(2,-1) are the vertices of triangleABC . Then the equation of the altitude from A to BC is :