Math Problem Statement

State whether the following statement is true or false: The point (-1,4) lies in quadrant IV of the Cartesian plane.

Solution

The question is asking if the point (1,4)(-1, 4) lies in Quadrant IV of the Cartesian plane.

In the Cartesian coordinate system:

  • Quadrant I: Both xx and yy are positive.
  • Quadrant II: xx is negative and yy is positive.
  • Quadrant III: Both xx and yy are negative.
  • Quadrant IV: xx is positive and yy is negative.

For the point (1,4)(-1, 4), the xx-coordinate is negative and the yy-coordinate is positive. Therefore, this point lies in Quadrant II, not Quadrant IV.

So, the correct answer is False.

Would you like more details, or do you have any further questions?

Here are 5 related questions to consider:

  1. How can you determine which quadrant a point belongs to?
  2. What are the coordinates of a point in Quadrant III?
  3. What is the significance of the sign of the coordinates in each quadrant?
  4. How does the Cartesian plane divide space into quadrants?
  5. What happens if a point lies on one of the axes?

Tip: To quickly determine a point's quadrant, check the signs of the xx and yy coordinates.

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Math Problem Analysis

Mathematical Concepts

Cartesian Coordinates
Quadrants

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8