For points `P-=(x_1, y_1)` and `Q-=(x_2, y_2)` of the coordinate plane,
a new distance `d(P ,Q)=|x_1-x_1|+|y_1-y_2|`. Let `O=(0,0)` and `A=(3,2)` .
Prove that the set of points in the first quadrant
which are equidistant (with respect to the new distance) from `O` and `A` consists of
the union of a line segment of finite length and an infinite ray.
Sketch this set in a labelled diagram.

For points P -= (x_(1) ,y_(1)) and Q = (x_(2),y_(2)) of the coordinate plane , a new distance d (P,Q) is defined by d(P,Q) = |x_(1)-x_(2)|+|y_(1)-y_(2)| Let O -= (0,0) ,A -= (1,2), B -= (2,3) and C-= (4,3) are four fixed points on x-y plane Let R(x,y) such that R is equidistant from the point O and A with respect to new distance and if 0 le x lt 1 and 0 le y lt 2 , then R lie on a line segment whose equation is

For points P -= (x_(1) ,y_(1)) and Q = (x_(2),y_(2)) of the coordinate plane , a new distance d (P,Q) is defined by d(P,Q) = |x_(1)-x_(2)|+|y_(1)-y_(2)| . Let O -= (0,0) ,A -= (1,2), B -= (2,3) and C-= (4,3) are four fixed points on x-y plane Let S(x,y) such that S is equidistant from points O and B with respect to new distance and if x ge 2 and 0 le y lt 3 then locus of S is

Three points P (h, k), Q(x_1, y_1) and R (x_2,y_2) lie on a line. Show that : (h-x_1)(y_2-y_1)= (k-y_1)(x_2-x_1) .

The coordinates of the image of the origin O with respect to the line x+y+1=0 are

If the points (x_1,y_1), (x_2,y_2) and (x_1 + x_2, y_1+y_2) are collinear, prove that x_1y_2 = x_2y_1

Let P be the point on the parabola y^(2)4x which is at the shortest distance from the center S of the circle x^(2)+y^(2)-4x-16y+64=0 . Let Q be the point on the circle dividing the line segment SP internally. Then

If P=(0,1,0) and Q=(0,0,1) then the projection of PQ on the plane x+y+z=3 is

The mid point of the line segment joining (2x,4) and (-2,3y) is (1,2x+1), then value of x and y are:

Find the equation of the planes parallel to the plane x-2y+2z-3=0 and which is at a unit distance from the point A(1,1,1) .

The length of projection of the line segment joining the points (1,0,-1) and (-1,2,2) on the plane x+3y-5z=6 is equal to