Find the area of the triangle `P Q R` with `Q(3,\ 2)` and the mid-points of the sides through `Q` being `(2,\ -1)` and `(1,\ 2)` .

Find the area of the triangle ABC with A(1,-4) and mid-points of sides through A being (2,-1)a n d(0,-1)dot

If a vertex of a triangle is (1, 1) and the mid-points of two side through this vertex are (-1, 2) and (3, 2), then centroid of the triangle is

Find the area of the triangle formed by the points P(-1. 5 ,\ 3),\ Q(6,\ -2)\ a n d\ R(-3,\ 4)dot

Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, 2) .

Write the position vector of the mid-point of the vector joining the points P (2, 3, 4) and Q (4, 1,-2).

Find the equation of the plane through the points P(1,\ 1,\ 0),\ Q(1,\ 2,\ 1)a n d\ R(-2,\ 2,\ -1)dot

Find the equation of line through the points P(2, -1, 4) and Q(6, 2, -3) in Cartesian form.

A straight line through the vertex P of a triangle P Q R intersects the side Q R at the points S and the cicumcircle of the triangle P Q R at the point Tdot If S is not the center of the circumcircle, then 1/(P S)+1/(S T) 2/(sqrt(Q SxxS R)) 1/(P S)+1/(S T) 4/(Q R)

In triangle P Q R , if P Q=R Q\ a n d\ L ,\ M\ a n d\ N are the mid-points of the sides P Q ,\ Q R\ a n d\ R P respectively. Prove that L N=M N .

Find the position vector of the mid point of the vector joining the points P(2,3,4)a n d\ Q(4,1,-2)dot