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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, logical reasoning, and competency-based concepts 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 (Final Revision & HOTS)
Based On: NCERT Latest Syllabus
Introduction:
The chapter Coordinate Geometry introduces students to the Cartesian coordinate system, where every point is represented by an ordered pair. In this final practice set, students will solve advanced concept-based questions involving quadrants, coordinate axes, reflections, distances, and logical reasoning. These questions are designed to strengthen conceptual understanding before examinations.
What You Will Learn?
✔ Coordinate Geometry Concepts
✔ Ordered Pairs
✔ Reflection of Points
✔ Coordinate Axes
✔ Distance from Axes
✔ Quadrant Identification
✔ Logical & Competency-Based Questions
✔ Final Exam Revision
Why This Topic Is Important?
Coordinate Geometry forms the base of graph-related mathematics. Mastering this chapter improves analytical thinking and prepares students for future topics such as linear equations, graph plotting, and geometry in higher classes.
Exam Relevance
These questions are useful for:
✔ CBSE Board Pattern
✔ State Board Exams
✔ School Tests
✔ Annual Examinations
✔ Olympiads
✔ Scholarship & NTSE Foundation
Q1. A point is 9 units to the left of the y-axis and 11 units above the x-axis. The coordinates of the point are:
A)
$$(-9,11)$$
B)
$$(9,11)$$
C)
$$(-11,9)$$
D)
$$(11,-9)$$
Answer:
$$(-9,11)$$
Useful Formula for this Question:
Distance from y-axis
$$=|x|$$
Distance from x-axis
$$=|y|$$
Solution:
The point is
- 9 units left of the y-axis
$$x=-9$$
- 11 units above the x-axis
$$y=11$$
Therefore, the coordinates are
$$(-9,11)$$
Hence, the correct answer is
$$(-9,11)$$
Q2. A point
$$(-8,6)$$
is reflected first in the y-axis and then in the x-axis. The final image is:
A)
$$(8,-6)$$
B)
$$(-8,-6)$$
C)
$$(8,6)$$
D)
$$(-6,8)$$
Answer:
$$(8,-6)$$
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
$$(-8,6)$$
Reflection in y-axis
$$(8,6)$$
Reflection in x-axis
$$(8,-6)$$
Hence, the correct answer is
$$(8,-6)$$
Q3. Which of the following points is equidistant from both coordinate axes and lies in the Second Quadrant?
A)
$$(-12,12)$$
B)
$$(12,12)$$
C)
$$(12,-12)$$
D)
$$(-12,-12)$$
Answer:
$$(-12,12)$$
Useful Formula for this Question:
Equal distance from both axes
$$|x|=|y|$$
Second Quadrant
$$(-,+)$$
Solution:
For
$$(-12,12)$$
$$|x|=|y|=12$$
The point lies in the Second Quadrant.
Hence, the correct answer is
$$(-12,12)$$
Q4. Which of the following statements is always true?
A) Every point on the x-axis is equidistant from both coordinate axes.
B) Every point on the y-axis has zero distance from the y-axis.
C) Every point in the Third Quadrant has equal coordinates.
D) Every point in the Fourth Quadrant is equally distant from both axes.
Answer:
Every point on the y-axis has zero distance from the y-axis.
Useful Formula for this Question:
Distance from y-axis
$$=|x|$$
Solution:
Every point on the y-axis has
$$x=0$$
Therefore,
$$|x|=0$$
Hence, its distance from the y-axis is zero.
Thus, the correct answer is:
Every point on the y-axis has zero distance from the y-axis.
Q5. Which one of the following points cannot lie in the Third Quadrant?
A)
$$(-7,-9)$$
B)
$$(-12,-5)$$
C)
$$(4,-8)$$
D)
$$(-10,-1)$$
Answer:
$$(4,-8)$$
Useful Formula for this Question:
Third Quadrant
$$(-,-)$$
Solution:
A point in the Third Quadrant must have
- Negative x-coordinate
- Negative y-coordinate
The point
$$(4,-8)$$
has a positive x-coordinate.
Therefore, it lies in the Fourth Quadrant.
Hence, the correct answer is
$$(4,-8)$$
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 can you identify the quadrant of a point quickly?
Answer:
Check the signs of the coordinates:
- First Quadrant → (+,+)
- Second Quadrant → (-,+)
- Third Quadrant → (-,-)
- Fourth Quadrant → (+,-)
Q. What is the distance of a point from the y-axis?
Answer:
The distance from the y-axis is the absolute value of its x-coordinate.
$$|x|$$
Q. Why are reflections important in Coordinate Geometry?
Answer:
Reflections help understand symmetry and transformations of points on the Cartesian plane. These concepts are widely used in higher mathematics and graph-related problems.
Common Mistakes Students Make
❌ Confusing the signs of coordinates in different quadrants.
❌ Forgetting that distance is always positive.
❌ Applying incorrect reflection rules.
❌ Assuming every point in a quadrant is equally distant from both axes.
❌ Mixing up the x-axis and y-axis while calculating 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
$$(x,y)\rightarrow(-x,y)$$
✔ 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
$$|x|=|y|$$
✔ Quadrant signs:
- First → (+,+)
- Second → (-,+)
- Third → (-,-)
- Fourth → (+,-)
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions serve as a comprehensive final revision of the chapter based on the latest NCERT syllabus. The questions are fresh, non-repeated, and competency-based, covering reflections, coordinate axes, quadrants, logical reasoning, and distance concepts. Completing all 15 practice sets will help students build strong conceptual clarity, improve problem-solving speed, and prepare confidently for CBSE board pattern questions, state board examinations, school tests, Olympiads, NTSE foundation, and scholarship exams.
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