For points 
and 
of the coordinate plane, a new distance 
is defined by 
. Let 
and 
. Consider the set of points 
in the first quadrant which are equidistant (with respect to the new distance) from 
and 
The set of points 
consists of
a)
One straight line only
b)
Union of two line segments
c)
Union of two infinite rays
d)
Union of a line segment of finite length and an infinite ray
For points and of the coordinate plane, a new distance is defined by . Let and . Consider the set of points in the first quadrant which are equidistant (with respect to the new distance) from and
The set of points consists of
a)
One straight line only
b)
Union of two line segments
c)
Union of two infinite rays
d)
Union of a line segment of finite length and an infinite ray
Question ID - 55406 | SaraNextGen Top Answer
For points and of the coordinate plane, a new distance is defined by . Let and . Consider the set of points in the first quadrant which are equidistant (with respect to the new distance) from and
The set of points consists of
a)
One straight line only
b)
Union of two line segments
c)
Union of two infinite rays
d)
Union of a line segment of finite length and an infinite ray
|
For points |
||
|
|
The set of points |
|
|
|
a) |
One straight line only |
|
|
b) |
Union of two line segments |
|
|
c) |
Union of two infinite rays |
|
|
d) |
Union of a line segment of finite length and an infinite ray |
(d)
.png)
Let 
be a general point in the first quadrant such that
(i)
[
and 
are +ve, point 
being in first quadrant]
If 
, then 
lies in region 
. Then,
If 
, then 
lies in region II. Then,
(not possible)
If 
then 
lies in region III. Then,
(not possible)
if 
, then 
lies in region IV. Then,
Hence, the required set consists of line segment 
of finite lengths as shown in the first region and the ray
in the fourth region
Obviously locus of 
is union of line segment and one infinite ray