Let `O` be the origin. If `A(1,0)a n dB(0,1)a n dP(x , y)` are points such that `x y >0a n dx+y<1,` then `P` lies either inside the triangle `O A B` o

Question

Let `O` be the origin. If `A(1,0)a n dB(0,1)a n dP(x , y)` are points such that `x y >0a n dx+y<1,` then `P` lies either inside the triangle `O A B` o

Let `O` be the origin. If `A(1,0)a n dB(0,1)a n dP(x , y)` are points such that `x y >0a n dx+y<1,` then `P` lies either inside the triangle `O A B` or in the third quadrant. `P` cannot lie inside the triangle `O A B` `P` lies inside the triangle `O A B` `P` lies in the first quadrant only
A. P lies either inside the triangle OAB or in the third quadrant
B. P cannot lie inside the triangle OAB
C. P lies inside the triangle OAB
D. P lies in the first quadrant only

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
Since `xy gt 0,` P lies either in the first quadrant or in the third quadrant. The inequality `x+y lt 1` represents all the points below the line x+y=1 so that `xy gt 0` and `x+y lt 1 imply that P lies either inside the triangle OAB or in the third quadrant.

4 views Answered 2023-02-05 15:29