If the coordiantes of two points A and B are (3,4) and (5, -2) respectively. Find the coordinates of any point P if PA = PB and area of `DeltaPAB =10` sq. units.

If the coordinates of two points A and B are (3,4) and (5,-2) respectively . Find the coordinates of any point 'c' , if AC =BC and area of triangle ABC =10 sq. units.

If A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P on AB such that AP = (3)/(7) AB.

The centroid of a triangle ABC is at the point (1,1,1) . If the coordinates of A and B are (3,-5,7) and (-1,7,-6) , respectively, find the coordinates of the point C.

If the x-coordinate of a point P on the join of Q(22,1)a n dR(5,1,-2)i s4, then find its z- coordinate.

If the coordinates of the points A,B,C,D be (1,2,3),(4,5,7),(-4,3,-6) and (2,9,2) respectively , then find the angle between the line AB and CD.

The coordinates of the point Aa n dB 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 A-P-Q-B, point P and Q trisects seg AB and A(3,1), Q(-1,3), then find coordinates of points B and P.

Let P(11, 7), Q(13.9, 4) an dR(9.5, 4) be the mid points of the sides AB, BC and AC respectively of triangleABC . Find the coordinates of the vertices A, B, and C. Hence find the area of triangleABC and compare this with area of trianglePQR .

If A and B be the points (3,4,5) and (-1,3,-7) , respectively, find the equation of the set of points P such that PA^(2)+PB^(2)=k^(2) , where k is a constant.