1. Every point that lies on the x-axis has its y-coordinate equal to:
- A0
- B1
- Cequal to its x-coordinate
- Dany non-zero number
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Answer: A) 0
A point on the x-axis is of the form (x, 0). Its distance from the x-axis (the y-coordinate) is 0.
Class 9 Points on the Axes — practice questions with answers
Coordinate Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. If the point P(a, 0) lies on the x-axis 5 units to the LEFT of the origin, then a equals:
- A-5
- B5
- C0
- D10
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Answer: A) -5
Points to the left of the origin on the x-axis have negative x-coordinates. So a = -5.
3. Which one of the following is the mirror image of the point (6, 0) about the y-axis?
- A(-6, 0)
- B(6, 0)
- C(0, 6)
- D(0, -6)
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Answer: A) (-6, 0)
Reflecting about the y-axis changes the sign of the x-coordinate, keeping y the same: (6, 0) -> (-6, 0). Both still lie on the x-axis.
4. A delivery boy starts at the origin, walks 9 units along the positive x-axis, then realises he is still on the x-axis. What are his coordinates, and what is his y-coordinate?
- A(9, 0); y-coordinate 0
- B(0, 9); y-coordinate 9
- C(9, 9); y-coordinate 9
- D(0, 0); y-coordinate 0
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Answer: A) (9, 0); y-coordinate 0
Walking only along the x-axis keeps y = 0. After 9 units to the right he is at (9, 0), y-coordinate 0.
5. A point A(k² - 9, 0) lies on the x-axis (which is automatic) and is exactly the origin. Find all possible values of k.
- Ak = 3 or k = -3
- Bk = 9 only
- Ck = 3 only
- Dk = 0 only
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Answer: A) k = 3 or k = -3
The y-coordinate is already 0, so A is on the x-axis. To be the origin, the abscissa must be 0: k² - 9 = 0 => k² = 9 => k = 3 or k = -3.
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