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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, coordinate axes, quadrants, 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:
The Coordinate Geometry chapter introduces students to the Cartesian coordinate system and develops the ability to represent geometric points using ordered pairs. This practice set includes competency-based questions that combine multiple concepts such as quadrants, reflections, coordinate axes, and distances. Solving these questions improves conceptual understanding and logical reasoning.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Ordered Pairs
✔ Coordinate Axes
✔ Reflection of Points
✔ Distance from Coordinate Axes
✔ Quadrant Analysis
✔ Competency-Based Questions
✔ HOTS Practice
Why This Topic Is Important?
Coordinate Geometry forms the basis of graph-based mathematics. Competency-based questions from this chapter test conceptual clarity rather than memorization. Practising such questions prepares students for school examinations and higher mathematics.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Olympiad & Scholarship Exams
Q1. A point is 7 units to the right of the y-axis and 11 units above the x-axis. If this point is reflected in the x-axis, the image will be:
A)
$$(7,-11)$$
B)
$$(-7,11)$$
C)
$$(-7,-11)$$
D)
$$(11,-7)$$
Answer:
$$(7,-11)$$
Useful Formula for this Question:
Reflection in the x-axis:
$$(x,y)\rightarrow(x,-y)$$
Solution:
The original point is
$$(7,11)$$
Reflection in the x-axis changes only the sign of the y-coordinate.
Therefore,
$$(7,11)\rightarrow(7,-11)$$
Hence, the correct answer is
$$(7,-11)$$
Q2. Which of the following points is 10 units from the x-axis but not 10 units from the y-axis?
A)
$$(10,10)$$
B)
$$(-4,-10)$$
C)
$$(-10,10)$$
D)
$$(10,-10)$$
Answer:
$$(-4,-10)$$
Useful Formula for this Question:
Distance from the x-axis
$$=|y|$$
Distance from the y-axis
$$=|x|$$
Solution:
For
$$(-4,-10)$$
Distance from the x-axis
$$=|-10|=10$$
Distance from the y-axis
$$=|-4|=4$$
Therefore, only the first condition is satisfied.
Hence, the correct answer is
$$(-4,-10)$$
Q3. Which point lies on the y-axis and remains unchanged after reflection in the y-axis?
A)
$$(5,0)$$
B)
$$(0,-9)$$
C)
$$(-7,7)$$
D)
$$(6,-6)$$
Answer:
$$(0,-9)$$
Useful Formula for this Question:
A point on the y-axis has
$$x=0$$
Solution:
The point
$$(0,-9)$$
lies on the y-axis.
Reflection in the y-axis does not change points on the y-axis.
Hence, the correct answer is
$$(0,-9)$$
Q4. Which of the following points lies in the Second Quadrant and is equidistant from both coordinate axes?
A)
$$(-13,13)$$
B)
$$(13,13)$$
C)
$$(-13,-13)$$
D)
$$(13,-13)$$
Answer:
$$(-13,13)$$
Useful Formula for this Question:
Second Quadrant
$$(-,+)$$
A point is equidistant from both axes if
$$|x|=|y|$$
Solution:
For
$$(-13,13)$$
Both conditions are satisfied:
- Second Quadrant ✔
- Equal distance from both axes ✔
Hence, the correct answer is
$$(-13,13)$$
Q5. Which one of the following statements is incorrect?
A) Every point on the x-axis has
$$y=0$$
B) Every point on the y-axis has
$$x=0$$
C) Reflection in the x-axis changes only the sign of the y-coordinate.
D) Every point reflected in the y-axis changes its y-coordinate.
Answer:
Every point reflected in the y-axis changes its y-coordinate.
Useful Formula for this Question:
Reflection in the y-axis
$$(x,y)\rightarrow(-x,y)$$
Solution:
Reflection in the y-axis changes only the sign of the x-coordinate.
The y-coordinate remains unchanged.
Therefore, statement D is incorrect.
Hence, the correct answer is:
Every point reflected in the y-axis changes its y-coordinate.
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
$$(x,y)\rightarrow(-x,-y)$$
Sign Convention
First Quadrant
$$(+,+)$$
Second Quadrant
$$(-,+)$$
Third Quadrant
$$(-,-)$$
Fourth Quadrant
$$(+,-)$$
FAQs
Q. Which coordinate changes during reflection in the y-axis?
Answer:
Only the x-coordinate changes its sign.
$$(x,y)\rightarrow(-x,y)$$
Q. Can a point on the x-axis remain unchanged after reflection in the x-axis?
Answer:
Yes. Every point with
$$y=0$$
remains unchanged after reflection in the x-axis.
Q. What condition must a point satisfy to be equidistant from both coordinate axes?
Answer:
A point is equidistant from both axes if
$$|x|=|y|$$
Common Mistakes Students Make
❌ Confusing reflections in the x-axis and y-axis.
❌ Forgetting to use absolute values for distances.
❌ Incorrectly identifying quadrants from the signs of coordinates.
❌ Assuming every point in a quadrant is equidistant from both axes.
❌ Mixing up the x-coordinate and y-coordinate.
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 means
$$|x|=|y|$$
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions – are prepared according to the latest NCERT syllabus and include fresh, advanced, and completely non-repeated questions. The MCQs focus on coordinate reasoning, reflections, coordinate axes, quadrants, and logical applications to strengthen conceptual understanding and improve performance in CBSE examinations, state board exams, Olympiads, and scholarship tests.
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