Problem 75 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The quadrants which satisfy the condition \(xy > 0\) are Quadrant I and Quadrant III.

Step 1: Analyze Sign of Coordinates in Each Quadrant

In Quadrant I, both x and y are positive, so the product xy is positive. In Quadrant II, x is negative and y is positive, so the product xy is negative. In Quadrant III, both x and y are negative, so the product xy is positive (because the product of two negatives is a positive). In Quadrant IV, x is positive and y is negative, so the product xy is negative.

Step 2: Determine Quadrants Where \(xy > 0\)

By analysing the sign of the product xy in each quadrant, Quadrant I and III satisfy the condition \(xy > 0\).