The coordinates of A and B are (1,3)and (2,1) respectively and P is a moving point on the straight line x+7y=12.Find the locus of the centroid of the triangle ABP.

If the vertices Pa n dQ of a triangle P Q R are given by (2, 5) and (4,-11) , respectively, and the point R moves along the line N given by 9x+7y+4=0 , then the locus of the centroid of triangle P Q R is a straight line parallel to PQ (b) QR (c) RP (d) N

The coordinates of the points A and B are (2,4) and (2,6) respectively . The point P is on that side of AB opposite to the origin . If PAB be an equilateral triangle , find the coordinates of P.

the coordinates of the vertices A,B,C of the triangle ABC are (7,-3) , (x,8) and (4,y) respectively , if the coordinates of the centroid of the triangle be (2,-1) , find x and y.

The coordinate of the vertices B and C of the triangle ABC are (5,2,8) and (2, -3, 4) respectively, if the coordinates of the centroid of the triangle are (3, -1,3), then the coordinates of the vertex A are-

The coordinates of the point A and B are (a,0) and (-a ,0), respectively. If a point P moves so that P A^2-P B^2=2k^2, when k is constant, then find the equation to the locus of the point Pdot

If (-4,7,5),(2,-6,-3) and (8,2,-5) are the coordinates of the mid points of the sides of a triangle, then find the coordinates of the centroid of the triangle.

If ( - 4 , 7 , 5) , ( 2 , - 6 , - 3) and ( 8 , 2 , - 5) are the coordinates of the mid-points of the sides of a triangle, then find the coordinates of the centroid of the triangle.

Find the coordinates of the foot of the perpendicular drawn from the point (2,-5) on the straight line x=y+1.

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is