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NO LINKS!! Describe the set of points P(x, y) in a coordinate plane that satisfy the given condition 4o​

NO LINKS!! Describe the set of points P(x, y) in a coordinate plane that satisfy the-example-1
User Jordan Walsh
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1 Answer

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9 votes

Answer:

(c) The set of all points in quadrants II and IV (x and y have opposite signs).

(d) The set of all points on the x-axis or y-axis.

Explanation:

The Cartesian plane is divided into four quadrants.

Quadrant I is where x and y are positive, and the rest of the quadrants follow in a counterclockwise direction.

  • Quadrant I: x > 0 and y > 0 → (x, y)
  • Quadrant II: x < 0 and y > 0 → (-x, y)
  • Quadrant III: x < 0 and y < 0 → (-x, -y)
  • Quadrant IV: x > 0 and y < 0 → (x, -y)

Part (c)

Given condition: xy < 0

For the given condition, x should be positive and y should be negative, or x should be negative and y should be positive, i.e. x and y should have opposite signs.

  • x is negative and y is positive in quadrant II.
  • x is positive and y is in negative quadrant IV.

Therefore, the description that satisfies the given condition is:

  • The set of all points in quadrants II and IV (x and y have opposite signs).

Part (d)

Given condition: xy = 0

For the given condition, x should be zero, or y should be zero, or x and y should both be zero.

  • x is zero for all points on the y-axis.
  • y is zero for all points on the x-axis.
  • x and y are both zero at the origin, which is on both axes.

Therefore, the description that satisfies the given condition is:

  • The set of all points on the x-axis or y-axis.
User Zavaz
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