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Practice Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers based on the latest NCERT syllabus. Solve final revision NCERT-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 (Final Revision & HOTS)
Based On: NCERT Latest Syllabus
Introduction:
The Coordinate Geometry chapter introduces students to the Cartesian coordinate system, where every point is represented by an ordered pair. This final practice set is designed as a comprehensive revision covering quadrants, coordinate axes, reflections, distances, and conceptual reasoning. Solving these questions will strengthen confidence and improve accuracy for school and competitive examinations.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Ordered Pairs
✔ Coordinate Axes
✔ Quadrant Identification
✔ Reflection of Points
✔ Distance from Coordinate Axes
✔ Competency-Based Questions
✔ Final Chapter Revision
Why This Topic Is Important?
Coordinate Geometry is the foundation of graph-based mathematics. A strong understanding of this chapter helps students solve graphical and algebraic problems in higher classes. This final practice set serves as an excellent revision before examinations.
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 16 units from the y-axis and 12 units below the x-axis. If it lies in the Fourth Quadrant, its coordinates are:
A)
$$(16,-12)$$
B)
$$(-16,-12)$$
C)
$$(12,-16)$$
D)
$$(-12,16)$$
Answer:
$$(16,-12)$$
Useful Formula for this Question:
Distance from the y-axis
$$=|x|$$
Distance from the x-axis
$$=|y|$$
Fourth Quadrant
$$(+,-)$$
Solution:
The point is 16 units from the y-axis.
Therefore,
$$|x|=16$$
Since it lies in the Fourth Quadrant,
$$x=16$$
The point is 12 units below the x-axis.
Therefore,
$$y=-12$$
Hence, the required coordinates are
$$(16,-12)$$
Q2. The reflection of the point
$$(14,-9)$$
in the y-axis is:
A)
$$(-14,-9)$$
B)
$$(14,9)$$
C)
$$(-14,9)$$
D)
$$(9,-14)$$
Answer:
$$(-14,-9)$$
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.
Thus,
$$(14,-9)\rightarrow(-14,-9)$$
Hence, the correct answer is
$$(-14,-9)$$
Q3. Which of the following points lies in the Third Quadrant and is equidistant from both coordinate axes?
A)
$$(-11,-11)$$
B)
$$(-11,11)$$
C)
$$(11,-11)$$
D)
$$(11,11)$$
Answer:
$$(-11,-11)$$
Useful Formula for this Question:
Third Quadrant
$$(-,-)$$
A point is equidistant from both axes if
$$|x|=|y|$$
Solution:
For
$$(-11,-11)$$
Both coordinates are negative.
Also,
$$|x|=|y|=11$$
Therefore, the point satisfies both conditions.
Hence, the correct answer is
$$(-11,-11)$$
Q4. Which of the following points lies on the positive x-axis?
A)
$$(20,0)$$
B)
$$(0,20)$$
C)
$$(-20,0)$$
D)
$$(0,-20)$$
Answer:
$$(20,0)$$
Useful Formula for this Question:
For every point on the x-axis,
$$y=0$$
Positive x-axis means
$$x>0$$
Solution:
The point
$$(20,0)$$
has
$$y=0$$
and
$$x>0$$
Therefore, it lies on the positive x-axis.
Hence, the correct answer is
$$(20,0)$$
Q5. Which one of the following statements is correct?
A) Every point on the x-axis has zero distance from the x-axis.
B) Reflection in the y-axis changes both coordinates.
C) Every point in the First Quadrant is equidistant from both coordinate axes.
D) Every point on the y-axis belongs to the Second Quadrant.
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 always true.
Therefore, 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. How do you identify the quadrant of a point?
Answer:
Look at the signs of the coordinates:
- First Quadrant → (+,+)
- Second Quadrant → (-,+)
- Third Quadrant → (-,-)
- Fourth Quadrant → (+,-)
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 coordinate axes belong to a quadrant?
Answer:
No. Any point lying on the x-axis or y-axis does not belong to any quadrant.
Common Mistakes Students Make
❌ Forgetting to use absolute values while finding distances.
❌ Confusing reflections in the x-axis and y-axis.
❌ Assigning incorrect signs to coordinates in different quadrants.
❌ Assuming every point in a quadrant is equally distant from both axes.
❌ Treating points on the coordinate axes as points in a quadrant.
Quick Revision Notes
✔ Distance from the x-axis
$$=|y|$$
✔ Distance from the y-axis
$$=|x|$$
✔ Reflection in the x-axis
$$(x,y)\rightarrow(x,-y)$$
✔ Reflection in the y-axis
$$(x,y)\rightarrow(-x,y)$$
✔ Reflection in both axes
$$(x,y)\rightarrow(-x,-y)$$
✔ Points on the coordinate axes do not belong to any quadrant.
✔ A point is equally distant from both axes if
$$|x|=|y|$$
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions – provide a comprehensive final revision of the chapter based on the latest NCERT syllabus. The questions are fresh, concept-based, and completely non-repeated, covering quadrants, coordinate axes, reflections, and distance concepts. Practising all 20 practice sets will strengthen conceptual understanding, improve problem-solving skills, and help students perform confidently in CBSE examinations, state board exams, school assessments, Olympiads, NTSE foundation, and scholarship examinations.
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