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:
- 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.
Let's check each point in the list:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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:
- Can a point lie on both the x-axis and y-axis simultaneously?
- What is the general form of points lying on the x-axis?
- How do you determine if a point lies on the line y = x?
- Can a point have a zero x-coordinate and lie on the x-axis?
- 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
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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