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Let A and B have coordinates (x(1) , y(1...

Let A and B have coordinates `(x_(1) , y_(1))` and `(x_(2) , y_(2))` respectively . We define the distance between A and B as
d (A , B) = max `{|x_(2) - x_(1)| , |y_(2) - y_(1)|}`
If d ( A, O) = 1 , where O is the origin , then the locus of A has an area of

A

1sq. Unit

B

2 sq. units

C

4sq. units

D

1/4 sq. units

Text Solution

Verified by Experts

The correct Answer is:
C
Let the coordinates of A be (h ,k) . Then ,
d(A,O) = 1
`implies ` max {|h| , |k|} = 1
`implies |h| le 1 `
`implies` Locus of A (h,k) is `|x| le 1 , |y| le 1`
Clearly , `|x| le 1` and `|y| le 1` represent the region enclosed by the square shown in fig. 40 .

`therefore` Area enclosed by the locus of A = `2 xx 2 = 4`sq. units
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