Problem 75
Question
List the quadrant or quadrants satisfying each condition. $$x y>0$$
Step-by-Step Solution
Verified Answer
The product of x and y will be positive in Quadrants I and III.
1Step 1: Identify Quadrants where both x and y are positive
In Quadrant I, both x and y coordinates are positive. As both coordinates are positive, their product would also be positive.
2Step 2: Identify Quadrants where both x and y are negative
In Quadrant III, both x and y coordinates are negative. A negative number times a negative number results in a positive number, so the product of x and y here would also be positive.
3Step 3: Analyze Quadrants where x and y have different signs
In Quadrant II (x is negative, y is positive) and Quadrant IV (x is positive, y is negative), the product of the x and y coordinates will be negative as a positive number times a negative number yields a negative result.
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