Home
Class 12
MATHS
Plot the region of the points P (x,y) sa...

Plot the region of the points P (x,y) satisfying `|x|+|y| lt 1.`

Text Solution

Verified by Experts

` (##CEN_CG_C02_S01_051_S01.png" width="80%">
Given that `|x|+|y| lt 1`.
We have four cases.
If x, `y gt 0`, then we have `x+y lt 1 " or " x+y-1 lt 0.`
Points satisfying these inequalities lie in triangular region in first quadrant formed by axes and line
x+y-1 = 0.
Similarly, we have three trinangular regions in all other quadrants.
Thus, points satisfying given inequality lie in a square as shown in the following figure.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXAMPLE|12 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.1|23 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

Plot the region of the points P(x,y) satisfying 2 gt max. {|x|, |y|}.

Sketch the region of the points satisfying max {|x|, |y|} le 4 .

Find tha area of the region containing the points (x, y) satisfying 4 le x^(2) + y^(2) le 2 (|x|+ |y|) .

Find the area of the region in which points satisfy 3 le |x| + |y| le 5.

Shade the regions where points satisfy |x-y| lt 1 .

Sketch the regions which points satisfy |x+y| ge 2 .

The locus of the point P(x,y) satisfying the relation sqrt((x-3) ^(2) +(y-1)^(2))+ sqrt((x+3) ^(2) +(y-1)^(2))=6 is-

Sketch the region satisfying |x| lt |y| .

Plot the region satisfying |x|+ |y| le 2 and |x|+|y| gt 2 .

Given that x in [0,1] and y in [0,1] . Let A be the event of selecting a point (x,y) satisfying y^(2) ge x and B be the event selecting a point (x,y) satisfying x^(2) ge y , then