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Chapter 1: Problem 14

Determine the quadrant(s) in which \((x, y)\) is Iocated so that the condition(s) is (are) satisfied. $$x y>0$$

Short Answer

Expert verified
The condition \(x y>0\) is satisfied in the 1st and 3rd quadrants.

Step by step solution

01

Analyzing the Signs in Each Quadrant

In the Cartesian coordinate system, each quadrant has specific sign rules for x and y coordinates. In the first quadrant, both x and y are positive. In the second quadrant, x is negative and y is positive. In the third quadrant, both x and y are negative. And in the fourth quadrant, x is positive and y is negative.
02

Where is the Product Positive?

Now, let's consider the condition given \(x y>0\). The product of x and y will be positive when both x and y have the same signs. This happens in two quadrants - the 1st quadrant where both are positive and 3rd quadrant where both are negative.
03

Conclusion

The condition \(x y>0\) is satisfied if and only if \((x, y)\) are in the 1st or 3rd quadrant of the Cartesian coordinate system. So the solution to this exercise is 1st and 3rd quadrants.

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