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Practice Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers based on the latest NCERT syllabus. Solve advanced, competency-based MCQs on coordinate geometry, quadrants, coordinate axes, reflections, and logical reasoning with detailed solutions for CBSE, state board, Olympiad, and scholarship exams.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Coordinate Geometry
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Difficult (Competency-Based & HOTS)
Based On: NCERT Latest Syllabus
Introduction:
Coordinate Geometry introduces students to the Cartesian plane, where each point is represented by an ordered pair. Advanced questions require understanding the relationship between coordinates, quadrants, reflections, and distances from the coordinate axes. This practice set strengthens conceptual clarity and develops logical reasoning for school and competitive examinations.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Ordered Pairs
✔ Reflection of Points
✔ Coordinate Axes
✔ Distance from Axes
✔ Quadrant Analysis
✔ Competency-Based Questions
✔ HOTS Practice
Why This Topic Is Important?
The concepts of Coordinate Geometry are used extensively in higher mathematics. Practising advanced MCQs helps students improve accuracy, reasoning ability, and confidence for competency-based examinations.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Unit Tests
✔ Annual Examinations
✔ Olympiad Preparation
✔ Scholarship Exams
Q1. A point is 12 units to the left of the y-axis and 9 units above the x-axis. The coordinates of the point are:
A)
$$(-12,9)$$
B)
$$(12,9)$$
C)
$$(-9,12)$$
D)
$$(9,-12)$$
Answer:
$$(-12,9)$$
Useful Formula for this Question:
Distance from the y-axis
$$=|x|$$
Distance from the x-axis
$$=|y|$$
Solution:
Since the point is 12 units left of the y-axis,
$$x=-12$$
Since it is 9 units above the x-axis,
$$y=9$$
Hence, the required point is
$$(-12,9)$$
Q2. Which of the following points remains unchanged after reflection in the x-axis?
A)
$$(-8,0)$$
B)
$$(0,5)$$
C)
$$(7,-4)$$
D)
$$(-3,9)$$
Answer:
$$(-8,0)$$
Useful Formula for this Question:
Reflection in the x-axis
$$(x,y)\rightarrow(x,-y)$$
A point remains unchanged if
$$y=0$$
Solution:
The point
$$(-8,0)$$
lies on the x-axis.
Reflection in the x-axis does not change any point lying on the x-axis.
Hence, the correct answer is
$$(-8,0)$$
Q3. Which of the following points lies exactly 8 units from both coordinate axes?
A)
$$(-8,8)$$
B)
$$(8,-6)$$
C)
$$(-6,-8)$$
D)
$$(10,8)$$
Answer:
$$(-8,8)$$
Useful Formula for this Question:
A point is equally distant from both axes if
$$|x|=|y|$$
Solution:
For
$$(-8,8)$$
Distance from the x-axis
$$=|8|=8$$
Distance from the y-axis
$$=|-8|=8$$
Therefore, the point is exactly 8 units from both coordinate axes.
Hence, the correct answer is
$$(-8,8)$$
Q4. A point is reflected in the y-axis and its image becomes
$$(15,-6)$$
The original point was:
A)
$$(-15,-6)$$
B)
$$(15,6)$$
C)
$$(-15,6)$$
D)
$$(-6,15)$$
Answer:
$$(-15,-6)$$
Useful Formula for this Question:
Reflection in the y-axis
$$(x,y)\rightarrow(-x,y)$$
Solution:
Only the sign of the x-coordinate changes during reflection in the y-axis.
If the reflected point is
$$(15,-6)$$
then the original point must be
$$(-15,-6)$$
Hence, the correct answer is
$$(-15,-6)$$
Q5. Which of the following statements is always true?
A) Every point on the x-axis has zero distance from the x-axis.
B) Every point in the Second Quadrant is equally distant from both axes.
C) Every point on the y-axis has positive y-coordinate.
D) Reflection in the y-axis changes both coordinates.
Answer:
Every point on the x-axis has zero distance from the x-axis.
Useful Formula for this Question:
Distance from the x-axis
$$=|y|$$
For every point on the x-axis,
$$y=0$$
Solution:
Every point on the x-axis has
$$y=0$$
Therefore,
$$|y|=0$$
Hence, its distance from the x-axis is zero.
The remaining statements are incorrect because they are not true for every point.
Hence, the correct answer is:
Every point on the x-axis has zero distance from the x-axis.
Important Formulas and Concepts
Ordered Pair
$$(x,y)$$
Origin
$$(0,0)$$
Distance from X-axis
$$|y|$$
Distance from Y-axis
$$|x|$$
Reflection in X-axis
$$(x,y)\rightarrow(x,-y)$$
Reflection in Y-axis
$$(x,y)\rightarrow(-x,y)$$
Reflection in Both Axes
$$(x,y)\rightarrow(-x,-y)$$
Quadrant Sign Convention
First Quadrant
$$(+,+)$$
Second Quadrant
$$(-,+)$$
Third Quadrant
$$(-,-)$$
Fourth Quadrant
$$(+,-)$$
FAQs
Q. Which points remain unchanged after reflection in the x-axis?
Answer:
Every point whose
$$y=0$$
(i.e., every point on the x-axis) remains unchanged after reflection in the x-axis.
Q. How can you identify whether a point is equidistant from both axes?
Answer:
A point is equidistant from both coordinate axes if
$$|x|=|y|$$
Q. Does reflection in the y-axis affect the y-coordinate?
Answer:
No. Reflection in the y-axis changes only the sign of the x-coordinate, while the y-coordinate remains unchanged.
Common Mistakes Students Make
❌ Confusing distance from the x-axis with distance from the y-axis.
❌ Forgetting to use absolute values while calculating distances.
❌ Applying the wrong reflection rule.
❌ Mixing up the sign conventions of quadrants.
❌ Assuming every point in a quadrant is equidistant from both axes.
Quick Revision Notes
✔ Distance from x-axis
$$=|y|$$
✔ Distance from y-axis
$$=|x|$$
✔ Reflection in x-axis
$$(x,y)\rightarrow(x,-y)$$
✔ Reflection in y-axis
$$(x,y)\rightarrow(-x,y)$$
✔ Reflection in both axes
$$(x,y)\rightarrow(-x,-y)$$
✔ Points on coordinate axes do not belong to any quadrant.
✔ Equal distance from both axes
$$|x|=|y|$$
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions – are prepared according to the latest NCERT syllabus and contain fresh, advanced, and completely non-repeated questions. The MCQs focus on coordinate reasoning, reflections, distances from coordinate axes, and quadrant analysis to strengthen conceptual understanding and improve performance in CBSE, state board, Olympiad, and scholarship examinations.
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