Name the quadrants in which signs of abscissa and ordinate are opposite
The Correct Answer and Explanation is:
Correct Answer:
Quadrants II and IV
Explanation
In the Cartesian coordinate system, the position of a point in a plane is described using two values:
- Abscissa (x-coordinate): represents the horizontal position.
- Ordinate (y-coordinate): represents the vertical position.
The plane is divided into four quadrants based on the signs of the x and y coordinates:
- Quadrant I: (+x, +y) → both abscissa and ordinate are positive.
- Quadrant II: (−x, +y) → abscissa is negative, ordinate is positive.
- Quadrant III: (−x, −y) → both abscissa and ordinate are negative.
- Quadrant IV: (+x, −y) → abscissa is positive, ordinate is negative.
The question asks for the quadrants in which the signs of the abscissa and ordinate are opposite. This occurs when one coordinate is positive and the other is negative. Let’s analyze:
- In Quadrant II, the abscissa is negative (−x) and the ordinate is positive (+y) → opposite signs.
- In Quadrant IV, the abscissa is positive (+x) and the ordinate is negative (−y) → again, opposite signs.
Therefore, the signs of the abscissa and ordinate are opposite in Quadrants II and IV.
This distinction is important in mathematics, especially in graphing functions and analyzing geometric relationships. Understanding the sign conventions in each quadrant helps with plotting points, interpreting vector directions, and solving equations graphically. For example, if you know a point lies in a quadrant where the signs of x and y are different, you can quickly narrow down possible locations, aiding in faster computation and error checking.
In summary, the signs of the abscissa and ordinate are opposite in Quadrant II (−x, +y) and Quadrant IV (+x, −y), which makes them the correct answer.
