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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 coordinate 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 chapter Coordinate Geometry develops students’ understanding of representing points on a Cartesian plane using ordered pairs. At an advanced level, students apply concepts of quadrants, reflections, coordinate axes, and distances to solve logical and analytical problems. These skills are essential for higher mathematics and competitive examinations.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Coordinate Reasoning
✔ Reflection of Points
✔ Distance from Coordinate Axes
✔ Logical Problems on Quadrants
✔ Symmetry of Points
✔ Sign Analysis
✔ Higher Order Thinking Skills (HOTS)
Why This Topic Is Important?
Coordinate Geometry is more than simply plotting points. Many examination questions test conceptual understanding, logical reasoning, and analytical thinking. A strong grasp of this chapter helps students solve advanced graph-based questions 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 (HOTS)
Q1. A point is 6 units from the x-axis and 8 units from the y-axis. If it lies in the Second Quadrant, its coordinates are:
A)
$$(-8,6)$$
B)
$$(8,6)$$
C)
$$(-6,8)$$
D)
$$(6,-8)$$
Answer:
$$(-8,6)$$
Useful Formula for this Question:
Distance from the x-axis
$$=|y|$$
Distance from the y-axis
$$=|x|$$
Second Quadrant
$$(-,+)$$
Solution:
Distance from the y-axis
$$=8$$
Therefore,
$$x=-8$$
Distance from the x-axis
$$=6$$
Therefore,
$$y=6$$
Hence, the required point is
$$(-8,6)$$
Q2. The reflection of the point
$$(-7,5)$$
first in the x-axis and then in the y-axis is:
A)
$$(7,-5)$$
B)
$$(-7,-5)$$
C)
$$(7,5)$$
D)
$$(-5,7)$$
Answer:
$$(7,-5)$$
Useful Formula for this Question:
Reflection in x-axis
$$(x,y)\rightarrow(x,-y)$$
Reflection in y-axis
$$(x,y)\rightarrow(-x,y)$$
Solution:
Initial point
$$(-7,5)$$
Reflection in x-axis
$$(-7,-5)$$
Reflection of this point in y-axis
$$(7,-5)$$
Hence, the correct answer is
$$(7,-5)$$
Q3. Which of the following points is equidistant from both axes but does not lie in the First Quadrant?
A)
$$(9,9)$$
B)
$$(-6,6)$$
C)
$$(8,-5)$$
D)
$$(-7,-3)$$
Answer:
$$(-6,6)$$
Useful Formula for this Question:
For equal distances,
$$|x|=|y|$$
Solution:
For
$$(-6,6)$$
$$|x|=|y|=6$$
The point lies in the Second Quadrant.
Hence, the correct answer is
$$(-6,6)$$
Q4. A point is reflected in the y-axis and its image becomes
$$(-11,-4)$$
The original point was:
A)
$$(11,-4)$$
B)
$$(-11,4)$$
C)
$$(11,4)$$
D)
$$(-4,-11)$$
Answer:
$$(11,-4)$$
Useful Formula for this Question:
Reflection in y-axis
$$(x,y)\rightarrow(-x,y)$$
Solution:
The reflected point is
$$(-11,-4)$$
Only the sign of the x-coordinate changes during reflection.
Therefore, the original point is
$$(11,-4)$$
Hence, the correct answer is
$$(11,-4)$$
Q5. Which of the following statements is correct?
A) Every point equidistant from both axes lies in the First Quadrant.
B) A point whose distance from the x-axis is zero must lie on the x-axis.
C) Reflection in the x-axis changes both coordinates.
D) Every point on the y-axis has positive y-coordinate.
Answer:
A point whose distance from the x-axis is zero must lie on the x-axis.
Useful Formula for this Question:
Distance from x-axis
$$=|y|$$
If
$$|y|=0$$
then
$$y=0$$
Solution:
A point having zero distance from the x-axis has
$$y=0$$
Such a point always lies on the x-axis.
The remaining statements are incorrect because:
- Equidistant points may lie in any quadrant.
- Reflection in the x-axis changes only the y-coordinate.
- A point on the y-axis may have positive, negative, or zero y-coordinate.
Hence, the correct answer is:
A point whose distance from the x-axis is zero must lie on 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
$$(x,y)\rightarrow(-x,y)$$
Sign Convention
First Quadrant
$$(+,+)$$
Second Quadrant
$$(-,+)$$
Third Quadrant
$$(-,-)$$
Fourth Quadrant
$$(+,-)$$
FAQs
Q. Can two different points have the same distance from both coordinate axes?
Answer:
Yes. Any points satisfying
$$|x|=|y|$$
are equidistant from both coordinate axes, even if they lie in different quadrants.
Q. How do reflections help in Coordinate Geometry?
Answer:
Reflections help determine the image of a point after flipping it across the x-axis or y-axis while preserving its distance from the respective axis.
Q. Why are absolute values used while calculating distances from axes?
Answer:
Distance is always non-negative. Therefore, absolute values are used to ensure the distance remains positive.
Common Mistakes Students Make
❌ Forgetting that distance is always positive.
❌ Confusing the sign changes during reflections.
❌ Selecting the wrong quadrant while determining coordinates.
❌ Ignoring the conditions given in the question.
❌ Assuming equal distances imply positive coordinates.
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
$$(x,y)\rightarrow(-x,y)$$
✔ A point with
$$y=0$$
lies on the x-axis.
✔ A point with
$$x=0$$
lies on the y-axis.
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions are designed according to the latest NCERT syllabus and include higher-level, concept-based, and non-repeated questions. They focus on logical reasoning, reflections, coordinate distances, and quadrant analysis, helping students strengthen their analytical thinking and prepare effectively for CBSE exams, state board examinations, Olympiads, NTSE foundation, and scholarship tests.
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