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Practice Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers based on the latest NCERT syllabus. Solve advanced and competency-based NCERT 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:
The Coordinate Geometry chapter introduces students to representing geometric points using the Cartesian coordinate system. Advanced questions in this chapter require students to apply multiple concepts such as quadrants, coordinate axes, reflections, and logical reasoning simultaneously. These skills form the foundation for higher mathematics and analytical geometry.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Coordinate Reasoning
✔ Reflection of Points
✔ Quadrant Analysis
✔ Distance from Coordinate Axes
✔ Logical Applications
✔ Competency-Based Questions
✔ HOTS Concepts
Why This Topic Is Important?
Coordinate Geometry develops visualization and analytical thinking. Competency-based questions from this chapter are frequently asked in CBSE examinations because they test conceptual understanding rather than memorization.
Exam Relevance
These questions are useful for:
✔ CBSE Board Pattern Questions
✔ State Board Exams
✔ School Unit Tests
✔ Annual Examinations
✔ Olympiad Preparation
✔ Scholarship & NTSE Foundation
Q1. A point is 8 units to the right of the y-axis and 6 units below the x-axis. In which quadrant does the point lie?
A) First Quadrant
B) Second Quadrant
C) Third Quadrant
D) Fourth Quadrant
Answer:
Fourth Quadrant
Useful Formula for this Question:
- Right of y-axis
$$x>0$$
- Below x-axis
$$y<0$$
Solution:
The point is
- 8 units to the right of the y-axis
$$x=8$$
- 6 units below the x-axis
$$y=-6$$
Thus, the coordinates are
$$(8,-6)$$
Since
$$x>0,;y<0$$
the point lies in the Fourth Quadrant.
Hence, the correct answer is:
Fourth Quadrant
Q2. The image of the point
$$(-4,-9)$$
after reflection in both coordinate axes is:
A)
$$(4,9)$$
B)
$$(-4,9)$$
C)
$$(4,-9)$$
D)
$$(-9,-4)$$
Answer:
$$(4,9)$$
Useful Formula for this Question:
Reflection in both axes
$$(x,y)\rightarrow(-x,-y)$$
Solution:
The point is
$$(-4,-9)$$
Changing the signs of both coordinates,
$$(-4,-9)\rightarrow(4,9)$$
Hence, the correct answer is
$$(4,9)$$
Q3. Which of the following points is 6 units away from both coordinate axes?
A)
$$(-6,6)$$
B)
$$(6,-8)$$
C)
$$(-5,-6)$$
D)
$$(8,6)$$
Answer:
$$(-6,6)$$
Useful Formula for this Question:
A point is equally distant from both axes if
$$|x|=|y|$$
Solution:
For
$$(-6,6)$$
Distance from the x-axis
$$=|6|=6$$
Distance from the y-axis
$$=|-6|=6$$
Both distances are equal to 6 units.
Hence, the correct answer is
$$(-6,6)$$
Q4. A point lies on the positive y-axis and is 15 units away from the origin. Its coordinates are:
A)
$$(15,0)$$
B)
$$(0,15)$$
C)
$$(-15,0)$$
D)
$$(0,-15)$$
Answer:
$$(0,15)$$
Useful Formula for this Question:
For every point on the y-axis,
$$x=0$$
Solution:
Since the point lies on the positive y-axis,
$$x=0$$
It is 15 units above the origin.
Therefore,
$$y=15$$
Hence, the point is
$$(0,15)$$
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) Every point equidistant from both coordinate axes satisfies
$$|x|=|y|$$
D) Every point in the First Quadrant is equidistant from both coordinate axes.
Answer:
Every point in the First Quadrant is equidistant from both coordinate axes.
Useful Formula for this Question:
Equal distances from both axes require
$$|x|=|y|$$
Solution:
A point in the First Quadrant can be
$$(2,8)$$
Here,
$$|2|\ne|8|$$
Therefore, it is not equidistant from both coordinate axes.
Thus, the statement is incorrect.
Hence, the correct answer is:
Every point in the First Quadrant is equidistant from both coordinate axes.
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. What is the image of a point after reflection in both axes?
Answer:
Both coordinates change their signs.
$$(x,y)\rightarrow(-x,-y)$$
Q. How do you know whether a point is equally distant from both coordinate axes?
Answer:
If
$$|x|=|y|$$
then the point is equally distant from both coordinate axes.
Q. Can a point on the x-axis belong to any quadrant?
Answer:
No. Points on the x-axis or y-axis do not belong to any quadrant.
Common Mistakes Students Make
❌ Forgetting that points on axes are not in any quadrant.
❌ Confusing distance from the x-axis with distance from the y-axis.
❌ Applying the wrong reflection rule.
❌ Ignoring absolute values while finding distances.
❌ Choosing the wrong signs according to the quadrant.
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 based on the latest NCERT syllabus and contain advanced, competency-based, and non-repeated questions. The MCQs focus on coordinate reasoning, quadrant identification, reflections, and logical applications to improve conceptual understanding and analytical skills. Regular practice of these questions will help students excel in CBSE board examinations, state board exams, Olympiads, NTSE foundation, and scholarship tests.
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