Home
Class 12
MATHS
For points P -= (x(1) ,y(1)) and Q = (x(...

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

A

(a) `x+y=3`

B

(b) `x+2y=3`

C

(c) `2x+y=3`

D

(d) `2x+2y=3`

Text Solution

Verified by Experts

The correct Answer is:
D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise The Straight Lines Exercise 3 : (Paragraph Based Questions)|3 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

Similar Questions

Explore conceptually related problems

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

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.

If P(x, y) is a point equidistant from the points A(6, -1) nad B(2, 3), show that x-y = 3.

Let P be (5, 3) and a point R on y=x and Q on the x-axis be such that P Q+Q R+R P is minimum. Then the coordinates of Q are

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) .

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

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

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

The coordinates of a point on the line (x-1)/(2)=(y+1)/(-3)=z at a distance 4sqrt(14) from the point (1, -1, 0) are

The distance of the plane 2x-y+2z+3=0 from the point (3,2,1) is

Home
Profile