Math Problem Statement

Which of the following points lie on (i) x-axis, (ii) y-axis? A(10, -2), B(5, 6), C(23, 0), D(0, 23), E(0, 4), F(6, 0), G(3, 0).

Solution

The question provided asks which points lie on the (i) x-axis and (ii) y-axis.

To determine this, let's recall the following:

  1. A point lies on the x-axis if its y-coordinate is 0.
  2. A point lies on the y-axis if its x-coordinate is 0.

Let's check each point in the list:

  1. A(10, -2): The y-coordinate is -2, so it does not lie on the x-axis. The x-coordinate is 10, so it does not lie on the y-axis.
  2. B(5, 6): The y-coordinate is 6, so it does not lie on the x-axis. The x-coordinate is 5, so it does not lie on the y-axis.
  3. C(23, 0): The y-coordinate is 0, so this point lies on the x-axis. The x-coordinate is 23, so it does not lie on the y-axis.
  4. D(0, 23): The y-coordinate is 23, so it does not lie on the x-axis. The x-coordinate is 0, so this point lies on the y-axis.
  5. E(0, 4): The y-coordinate is 4, so it does not lie on the x-axis. The x-coordinate is 0, so this point lies on the y-axis.
  6. F(6, 0): The y-coordinate is 0, so this point lies on the x-axis. The x-coordinate is 6, so it does not lie on the y-axis.
  7. G(3, 0): The y-coordinate is 0, so this point lies on the x-axis. The x-coordinate is 3, so it does not lie on the y-axis.

Final Answer:

  • Points on the x-axis: C(23, 0), F(6, 0), G(3, 0)
  • Points on the y-axis: D(0, 23), E(0, 4)

Let me know if you'd like more details or explanations. Here are some related questions for further practice:

  1. Can a point lie on both the x-axis and y-axis simultaneously?
  2. What is the general form of points lying on the x-axis?
  3. How do you determine if a point lies on the line y = x?
  4. Can a point have a zero x-coordinate and lie on the x-axis?
  5. How does the distance of a point from the origin affect whether it lies on either axis?

Tip: Always remember that any point on the x-axis will have a zero y-coordinate, and any point on the y-axis will have a zero x-coordinate!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Points on the X-axis and Y-axis

Formulas

-

Theorems

A point lies on the x-axis if its y-coordinate is 0
A point lies on the y-axis if its x-coordinate is 0

Suitable Grade Level

Grades 6-8