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Practice Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers based on the latest NCERT syllabus. Solve advanced NCERT-based MCQs on coordinate geometry, quadrants, reflections, coordinate axes, 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 is one of the most logical chapters in Class 9 Mathematics. Students learn to represent points on the Cartesian plane and solve problems based on coordinates, quadrants, reflections, and distances from coordinate axes. This practice set contains higher-level conceptual questions designed to improve reasoning skills and exam performance.
What You Will Learn?
✔ Coordinate Plane
✔ Ordered Pairs
✔ Reflection of Points
✔ Distance from Coordinate Axes
✔ Quadrant Identification
✔ Coordinate Logic
✔ HOTS Questions
✔ Exam-Oriented Practice
Why This Topic Is Important?
Many competency-based questions in school examinations require students to analyze coordinate positions instead of simply remembering formulas. Regular practice improves conceptual clarity and logical thinking.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ Unit Tests
✔ Annual Exams
✔ Olympiad Preparation
✔ Scholarship Exams
Q1. A point is 13 units from the y-axis and 7 units below the x-axis. If it lies in the Fourth Quadrant, its coordinates are:
A)
$$(13,-7)$$
B)
$$(-13,-7)$$
C)
$$(7,-13)$$
D)
$$(-7,13)$$
Answer:
$$(13,-7)$$
Useful Formula for this Question:
Distance from y-axis
$$=|x|$$
Distance from x-axis
$$=|y|$$
Fourth Quadrant
$$(+,-)$$
Solution:
Distance from the y-axis is
$$13$$
Therefore,
$$x=13$$
Distance from the x-axis is
$$7$$
Since the point is below the x-axis,
$$y=-7$$
Hence, the point is
$$(13,-7)$$
Q2. Which point remains unchanged after reflection in the y-axis?
A)
$$(0,8)$$
B)
$$(6,0)$$
C)
$$(-5,7)$$
D)
$$(4,-9)$$
Answer:
$$(0,8)$$
Useful Formula for this Question:
Reflection in y-axis
$$(x,y)\rightarrow(-x,y)$$
A point remains unchanged only if
$$x=0$$
Solution:
The point
$$(0,8)$$
lies on the y-axis.
Reflection in the y-axis does not change points lying on the y-axis.
Hence, the correct answer is
$$(0,8)$$
Q3. Which of the following points is not possible if the point is equidistant from both coordinate axes?
A)
$$(9,9)$$
B)
$$(-11,11)$$
C)
$$(8,-8)$$
D)
$$(10,-6)$$
Answer:
$$(10,-6)$$
Useful Formula for this Question:
A point is equidistant from both axes if
$$|x|=|y|$$
Solution:
For
$$(10,-6)$$
$$|10|\ne|6|$$
Hence, it is not equidistant from both coordinate axes.
Therefore, the correct answer is
$$(10,-6)$$
Q4. A point lies on the negative x-axis and is 14 units from the origin. Its coordinates are:
A)
$$(-14,0)$$
B)
$$(14,0)$$
C)
$$(0,-14)$$
D)
$$(0,14)$$
Answer:
$$(-14,0)$$
Useful Formula for this Question:
For every point on the x-axis,
$$y=0$$
Negative x-axis means
$$x<0$$
Solution:
The point lies on the x-axis.
Therefore,
$$y=0$$
It is on the negative side.
Hence,
$$x=-14$$
The required point is
$$(-14,0)$$
Q5. Which statement is always correct?
A) Reflection in both axes changes only the x-coordinate.
B) Every point on the x-axis remains unchanged after reflection in the x-axis.
C) Every point on the y-axis belongs to the Second Quadrant.
D) Every point in the Fourth Quadrant is equidistant from both axes.
Answer:
Every point on the x-axis remains unchanged after reflection in the x-axis.
Useful Formula for this Question:
Reflection in x-axis
$$(x,y)\rightarrow(x,-y)$$
If
$$y=0$$
the point remains unchanged.
Solution:
Points on the x-axis have
$$y=0$$
Changing the sign of zero gives zero.
Therefore, the point remains unchanged.
Hence, the correct answer is:
Every point on the x-axis remains unchanged after reflection in 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:
All points lying on the x-axis remain unchanged because their y-coordinate is zero.
Q. Can a point on the y-axis belong to any quadrant?
Answer:
No. A point on the y-axis does not belong to any quadrant.
Q. How do you identify whether a point is equidistant from both coordinate axes?
Answer:
Check whether
$$|x|=|y|$$
If both absolute values are equal, the point is equidistant from both coordinate axes.
Common Mistakes Students Make
❌ Forgetting that points on coordinate axes are not in any quadrant.
❌ Using signed values instead of absolute values while calculating distances.
❌ Confusing reflections in the x-axis and y-axis.
❌ Ignoring the quadrant while assigning coordinate signs.
❌ Assuming every point with positive coordinates 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 axes are not part of any quadrant.
✔ Equal distance from both axes
$$|x|=|y|$$
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions – contain fresh, advanced, and completely non-repeated NCERT-based questions. This set focuses on competency-based learning, coordinate reasoning, reflections, and quadrant analysis to strengthen conceptual understanding. Practising all 20 practice sets will provide excellent preparation for CBSE exams, state board examinations, school assessments, Olympiads, NTSE foundation, and scholarship examinations.
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