First slide

Equation of line in Straight lines

Question

Let O be the origin, $A (1, 0)$ and $B (0, 1)$ and $P (x, y)$ are points such that $x y > 0$ and $x + y < 1$ , then

Moderate

A

P lies either inside the triangle OAB or in the third quad rant
B

P cannot lie inside the triangle OAB
C

P lies inside the triangle OAB
D

lies in the first quadrant only

Solution

Since $x y > 0, P$ either lies in the first quadrant or in the third quadrant. The inequality $x + y < 1$ represents all points below the line $x + y = 1$ . So that $x y > 0$ and $x + y < 1$ imply that either P lies inside the triangle OAB or in the third quadrant.

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