In the figure, OB is the perpendicular bisector of the line segment DE. `FA_|_OB` and FE intersects OB at point C. Prove that `1/(OA)+1/(OB)=2/(OC)`.

Find the equation of the perpendicular bisector of the line segment joining (7,1) and (3,5) .

The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is :

If 2 x+3 y+4=0 is the perpendicular bisector of the segment joining the points A(1,2) and B(alpha, beta) then the value of alpha+beta is

Find the coordinates of the points of trisection of the line segment joining A(4,-1) and B(-2,-3) .

If vec OA = i-j and vec OB = j-k , the unit vector perpendicular to the plane AOB is

Find the equation of the right bisector of the line segment joining the points (3, 4) " and " (-1, 2) .

In Figure , POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that lfloorROS=(1)/(2)(lfloorQOS-lfloorPOS)

If p is the length of perpendicular from origin to the line whose intercepts on the axes are 'a' and 'b' then prove that (1)/(p^(2)) = (1)/(a^(2)) + (1)/(b^(2)) .

Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).

The perpendicular from the origin to the line y = mx + c meets it at the point (-1, 2) . Find the values of m and c.