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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 develops students’ understanding of the Cartesian plane by representing points through ordered pairs. This advanced practice set combines concepts such as quadrants, coordinate axes, reflections, and distances into competency-based questions that enhance logical reasoning and mathematical accuracy.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Ordered Pairs
✔ Quadrant Identification
✔ Reflection of Points
✔ Distance from Coordinate Axes
✔ Coordinate Reasoning
✔ Competency-Based Questions
✔ HOTS Practice
Why This Topic Is Important?
Coordinate Geometry is the foundation of graph-based mathematics. A clear understanding of coordinates and reflections helps students solve more advanced mathematical problems in higher classes. Regular practice also improves speed and accuracy in 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 15 units from the y-axis and 3 units above the x-axis. If it lies in the Second Quadrant, its coordinates are:
A)
$$(-15,3)$$
B)
$$(15,3)$$
C)
$$(-3,15)$$
D)
$$(15,-3)$$
Answer:
$$(-15,3)$$
Useful Formula for this Question:
Distance from the y-axis
$$=|x|$$
Distance from the x-axis
$$=|y|$$
Second Quadrant
$$(-,+)$$
Solution:
The point is 15 units from the y-axis.
Therefore,
$$|x|=15$$
Since it lies in the Second Quadrant,
$$x=-15$$
The point is 3 units above the x-axis.
Therefore,
$$y=3$$
Hence, the required coordinates are
$$(-15,3)$$
Q2. The reflection of the point
$$(-9,5)$$
in the x-axis is:
A)
$$(9,5)$$
B)
$$(-9,-5)$$
C)
$$(9,-5)$$
D)
$$(-5,-9)$$
Answer:
$$(-9,-5)$$
Useful Formula for this Question:
Reflection in the x-axis
$$(x,y)\rightarrow(x,-y)$$
Solution:
The x-coordinate remains unchanged.
The sign of the y-coordinate changes.
Thus,
$$(-9,5)\rightarrow(-9,-5)$$
Hence, the correct answer is
$$(-9,-5)$$
Q3. Which of the following points is 7 units from both coordinate axes?
A)
$$(7,-7)$$
B)
$$(7,-5)$$
C)
$$(-7,4)$$
D)
$$(5,7)$$
Answer:
$$(7,-7)$$
Useful Formula for this Question:
A point is equally distant from both coordinate axes if
$$|x|=|y|$$
Solution:
For
$$(7,-7)$$
Distance from the x-axis
$$=|-7|=7$$
Distance from the y-axis
$$=|7|=7$$
Therefore, the point is 7 units from both coordinate axes.
Hence, the correct answer is
$$(7,-7)$$
Q4. Which of the following points lies on the negative y-axis?
A)
$$(0,-18)$$
B)
$$(-18,0)$$
C)
$$(18,0)$$
D)
$$(0,18)$$
Answer:
$$(0,-18)$$
Useful Formula for this Question:
For every point on the y-axis,
$$x=0$$
Negative y-axis means
$$y<0$$
Solution:
The point
$$(0,-18)$$
has
$$x=0$$
and
$$y<0$$
Therefore, it lies on the negative y-axis.
Hence, the correct answer is
$$(0,-18)$$
Q5. Which of the following statements is always true?
A) Every point in the Fourth Quadrant has equal distances from both axes.
B) Every point on the y-axis has zero distance from the y-axis.
C) Reflection in the x-axis changes both coordinates.
D) Every point in the First Quadrant satisfies
$$|x|=|y|$$
Answer:
Every point on the y-axis has zero distance from the y-axis.
Useful Formula for this Question:
Distance from the y-axis
$$=|x|$$
For every point on the y-axis,
$$x=0$$
Solution:
Every point on the y-axis has
$$x=0$$
Therefore,
$$|x|=0$$
Hence, the distance from the y-axis is zero.
The remaining statements are not always true.
Therefore, the correct answer is:
Every point on the y-axis has zero distance from the y-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 coordinate changes during reflection in the x-axis?
Answer:
Only the sign of the y-coordinate changes.
$$(x,y)\rightarrow(x,-y)$$
Q. Can a point on the y-axis have a positive or negative y-coordinate?
Answer:
Yes. A point on the y-axis has
$$x=0$$
while the y-coordinate may be positive, negative, or zero.
Q. What condition must be satisfied for a point to be equally distant from both coordinate axes?
Answer:
The point must satisfy
$$|x|=|y|$$
Common Mistakes Students Make
❌ Confusing the sign conventions of different quadrants.
❌ Forgetting that distance is measured using absolute values.
❌ Changing both coordinates during reflection in the x-axis.
❌ Assuming every point in a quadrant is equally distant from both axes.
❌ Confusing points on the coordinate axes with points in quadrants.
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.
✔ Equal distance from both axes
$$|x|=|y|$$
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions – are based on the latest NCERT syllabus and contain fresh, advanced, and non-repeated questions. The MCQs strengthen concepts related to coordinate axes, quadrants, reflections, and logical reasoning, helping students prepare effectively for CBSE examinations, state board exams, Olympiads, scholarship tests, and other competency-based assessments.
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