P and Q are points on the line joining `A(-2,5)` and `B(3,1)` such that `AP=PQ=QB`. Then, the distance of the midpoint of PQ from the origin is

P and Q are points on the line joining A(-2,5) and B(3,1) such that A P=P Q=Q B . Then, the distance of the midpoint of P Q from the origin is 3 (b) (sqrt(37))/2 (b) 4 (d) 3.5

P and Q are such two points on the line segment obtained by joining the points A (-2, 5) and B (3, 1) that AP = PQ = QB. Then find the coordinates of the mid-point of PQ.

Q, R, S are the points on the line joining the point P(a,x) and T(b,y) such that PQ=QR=RS=ST, then ((5a+3b)/8, (5x+3y)/8) is the midpoint of the segment

Show that the relation R in the set A of points in a plane given by R = {(P,Q): distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

Find the equation of the perpendicular bisector of the straight line -segment joining the points (-2,7) and(8,-1) . Also find the distance of this bisector from the origin .

AB is a line - segment. P and Q are points on either side of AB such that each of them is equidistant from the points A and B. Show that the line PQ is the perpendicular bisector of AB.

Find the equation of the plane passing through the point A(1,2,1) and perpendicular to the line joining the points P(1,4,2) and Q (2,3,5) . Also , find the distance of this plane from the line (x+3)/(2)=(y-5)/(-1)=(z-7)/(-1) .

Find the equation of the plane passing through the points (2,1,0),(5,0,1) and (4,1,1) If P is the point (2,1,6) then find point Q such that PQ is perpendicular to the above plane and the mid point of PQ lies on it.

Find the equation of the straight line which divides perpendicularly the straight line -segment joining the points (7,9) and (-1,-7) internally in the ratio 3 :5 . What is the distance of this line from origin?

P divides the line segment joinign the points A(1,2,5) and B(6,7,-5) in the ratio 2:3 . If Q be the mid point of the segment AB then the coordinates of P and Q will be