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Chapter 1: Problem 75

List the quadrant or quadrants satisfying each condition. $$x y>0$$

Short Answer

Expert verified
The condition, x*y > 0 is satisfied in Quadrant I and Quadrant III of the Cartesian Plane.

Step by step solution

01

Understanding the Cartesian Plane

The Cartesian Plane comprises four quadrants: Quadrant I where x>0 and y>0; Quadrant II where x<0 and y>0; Quadrant III where x<0 and y<0; and Quadrant IV where x>0 and y<0. The condition xy > 0 signifies that x and y are of the same sign.
02

Identifying the Quadrants

We need to identify the quadrants where both x and y are either positive or negative. In the first quadrant (Quadrant I), both x and y are positive. So, their product will be positive. In the third quadrant (Quadrant III), both x and y are negative. But the product of two negative numbers is also positive. Therefore, x*y will be positive in both these quadrants.

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