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Practice Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers based on the latest NCERT syllabus. Solve challenging NCERT-based MCQs on coordinate geometry, quadrants, reflections, distances from axes, and logical reasoning with detailed solutions for CBSE and state board exams.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Coordinate Geometry
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Difficult
Based On: NCERT Latest Syllabus
Introduction:
The Coordinate Geometry chapter provides the foundation for representing points on a plane using ordered pairs. In advanced questions, students must apply multiple concepts such as quadrant identification, distances from coordinate axes, reflections, and logical reasoning together. These skills are essential for scoring well in school examinations and developing problem-solving abilities.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Ordered Pairs
✔ Coordinate Reasoning
✔ Distance from Coordinate Axes
✔ Reflection of Points
✔ Logical Analysis of Coordinates
✔ Quadrant Identification
✔ Higher Order Thinking Skills (HOTS)
Why This Topic Is Important?
Coordinate Geometry is a concept-based chapter. Rather than relying on memorization, students must understand the relationship between coordinates, axes, and quadrants. Strong conceptual knowledge makes advanced graph-based mathematics much easier in higher classes.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ State Board Exams
✔ School Olympiads
✔ NTSE Foundation
✔ Scholarship Exams
✔ Higher Order Thinking Questions (HOTS)
Q1. A point is 10 units from the y-axis and 4 units below the x-axis. If it lies in the Fourth Quadrant, its coordinates are:
A)
$$(10,-4)$$
B)
$$(-10,-4)$$
C)
$$(4,-10)$$
D)
$$(-4,10)$$
Answer:
$$(10,-4)$$
Useful Formula for this Question:
Distance from y-axis
$$=|x|$$
Distance from x-axis
$$=|y|$$
Fourth Quadrant
$$(+,-)$$
Solution:
The point is 10 units from the y-axis.
Therefore,
$$|x|=10$$
Since it lies in the Fourth Quadrant,
$$x=10$$
It is 4 units below the x-axis.
Hence,
$$y=-4$$
Therefore, the required point is
$$(10,-4)$$
Q2. The reflection of the point
$$(6,-8)$$
first in the y-axis and then in the x-axis is:
A)
$$(-6,8)$$
B)
$$(6,8)$$
C)
$$(-6,-8)$$
D)
$$(8,-6)$$
Answer:
$$(-6,8)$$
Useful Formula for this Question:
Reflection in y-axis
$$(x,y)\rightarrow(-x,y)$$
Reflection in x-axis
$$(x,y)\rightarrow(x,-y)$$
Solution:
Initial point
$$(6,-8)$$
Reflection in y-axis
$$(-6,-8)$$
Reflection in x-axis
$$(-6,8)$$
Hence, the correct answer is
$$(-6,8)$$
Q3. Which of the following points is equidistant from both coordinate axes and lies in the Fourth Quadrant?
A)
$$(-7,-7)$$
B)
$$(9,-9)$$
C)
$$(5,8)$$
D)
$$(-6,6)$$
Answer:
$$(9,-9)$$
Useful Formula for this Question:
For equal distances,
$$|x|=|y|$$
Fourth Quadrant
$$(+,-)$$
Solution:
For
$$(9,-9)$$
$$|x|=|y|=9$$
The point lies in the Fourth Quadrant.
Hence, the correct answer is
$$(9,-9)$$
Q4. A point lies on the negative y-axis and is 12 units away from the origin. Which point represents it?
A)
$$(0,-12)$$
B)
$$(-12,0)$$
C)
$$(12,0)$$
D)
$$(0,12)$$
Answer:
$$(0,-12)$$
Useful Formula for this Question:
For any point on the y-axis,
$$x=0$$
Negative y-axis means
$$y<0$$
Solution:
The point lies on the y-axis.
Therefore,
$$x=0$$
Since it is on the negative y-axis and 12 units away from the origin,
$$y=-12$$
Hence, the point is
$$(0,-12)$$
Q5. Which of the following statements is false?
A) Every point on the y-axis has
$$x=0$$
B) Reflection in the x-axis changes the sign of the y-coordinate.
C) Every point equidistant from both axes satisfies
$$|x|=|y|$$
D) Every point in the Third Quadrant is equidistant from both coordinate axes.
Answer:
Every point in the Third Quadrant is equidistant from both coordinate axes.
Useful Formula for this Question:
For equal distances,
$$|x|=|y|$$
Solution:
Only those points for which
$$|x|=|y|$$
are equidistant from both coordinate axes.
A point in the Third Quadrant may have coordinates such as
$$(-4,-9)$$
where
$$|x|\ne|y|$$
Therefore, the statement is false.
Hence, the correct answer is:
Every point in the Third 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
$$(x,y)\rightarrow(-x,y)$$
Sign Convention
First Quadrant
$$(+,+)$$
Second Quadrant
$$(-,+)$$
Third Quadrant
$$(-,-)$$
Fourth Quadrant
$$(+,-)$$
FAQs
Q. What is the distance of a point from the origin?
Answer:
This chapter mainly focuses on locating points and distances from the coordinate axes. The distance from the origin is studied in detail in higher classes.
Q. Can a point lie on both the x-axis and the y-axis?
Answer:
Yes. Only the origin
$$(0,0)$$
lies on both the x-axis and the y-axis.
Q. Why is the absolute value used while finding the distance from an axis?
Answer:
Distance is always non-negative, so absolute values are used to ensure the distance remains positive.
Common Mistakes Students Make
❌ Confusing the positive and negative directions of the axes.
❌ Forgetting the sign changes during reflections.
❌ Ignoring the quadrant while determining coordinates.
❌ Assuming every point in a quadrant has equal distances from both axes.
❌ Using negative values for distances.
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
$$(x,y)\rightarrow(-x,y)$$
✔ Origin
$$(0,0)$$
✔ 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 include challenging, concept-oriented, and non-repeated questions. The MCQs emphasize logical reasoning, reflections, coordinate distances, and quadrant analysis to strengthen students’ conceptual understanding. Regular practice of these questions will help students perform confidently in CBSE exams, state board examinations, Olympiads, NTSE foundation, and scholarship tests.
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