Math Problem Statement

Name the quadrant or axis where each point lies. (Points: C, K, Q, T)

Solution

In this graph, you need to identify the quadrant or axis where each point lies. Here's how we determine this:

  • Quadrants:
    • Quadrant I: x>0x > 0, y>0y > 0
    • Quadrant II: x<0x < 0, y>0y > 0
    • Quadrant III: x<0x < 0, y<0y < 0
    • Quadrant IV: x>0x > 0, y<0y < 0

Let's examine each point:

  1. Point C is at approximately (2,2)(2, 2), which places it in Quadrant I.
  2. Point K is at approximately (6,2)(6, -2), which places it in Quadrant IV.
  3. Point Q is at approximately (4,6)(4, 6), which places it in Quadrant I.
  4. Point T is at approximately (4,4)(-4, -4), which places it in Quadrant III.

So the quadrants or axes for each point are:

  • Point C: Quadrant I
  • Point K: Quadrant IV
  • Point Q: Quadrant I
  • Point T: Quadrant III

Let me know if you'd like further clarification or details. Here are five related questions to expand your understanding:

  1. What would happen if a point lies on the axis?
  2. How do you determine if a point lies in a specific quadrant based on its coordinates?
  3. Can a point ever belong to more than one quadrant?
  4. How would the quadrants change if the coordinate plane was rotated 90 degrees?
  5. What is the significance of the origin, and how is it related to the quadrants?

Tip: Always remember, the sign of the coordinates determines the quadrant: positive xx and yy for Quadrant I, negative xx and positive yy for Quadrant II, and so on!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Quadrants
Axes

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8