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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, quadrants, coordinate axes, reflections, and logical reasoning with detailed solutions for CBSE, state board, and school exams.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Coordinate Geometry
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Difficult (HOTS)
Based On: NCERT Latest Syllabus
Introduction:
The Coordinate Geometry chapter helps students understand the relationship between algebra and geometry through the Cartesian coordinate system. At the advanced level, students are expected to analyze coordinate positions, identify quadrants, determine reflections, and solve logical problems based on distances from coordinate axes. These concepts strengthen mathematical reasoning and prepare students for higher-level mathematics.
What You Will Learn?
✔ Coordinate Reasoning
✔ Cartesian Plane
✔ Reflection of Points
✔ Distance from Coordinate Axes
✔ Quadrant Analysis
✔ Ordered Pair Concepts
✔ HOTS-Based Coordinate Problems
✔ Board Exam Preparation
Why This Topic Is Important?
Coordinate Geometry is one of the fundamental chapters of mathematics. Many school examinations now include competency-based and HOTS questions that require conceptual understanding rather than direct formulas. Regular practice improves analytical thinking and accuracy.
Exam Relevance
These questions are useful for:
✔ CBSE Competency-Based Questions
✔ State Board Exams
✔ Unit Tests
✔ Annual Examinations
✔ Olympiad Preparation
✔ Scholarship & NTSE Foundation
Q1. A point is 5 units from the x-axis and 9 units from the y-axis. If it lies in the Third Quadrant, the coordinates of the point are:
A)
$$(-9,-5)$$
B)
$$(-5,-9)$$
C)
$$(9,-5)$$
D)
$$(-9,5)$$
Answer:
$$(-9,-5)$$
Useful Formula for this Question:
Distance from x-axis
$$=|y|$$
Distance from y-axis
$$=|x|$$
Third Quadrant
$$(-,-)$$
Solution:
Distance from the y-axis is
$$9$$
Therefore,
$$|x|=9$$
Since the point lies in the Third Quadrant,
$$x=-9$$
Distance from the x-axis is
$$5$$
Therefore,
$$y=-5$$
Hence, the point is
$$(-9,-5)$$
Q2. A point is reflected first in the x-axis and then in the y-axis. Which transformation takes place?
A)
$$(x,y)\rightarrow(-x,-y)$$
B)
$$(x,y)\rightarrow(x,-y)$$
C)
$$(x,y)\rightarrow(-x,y)$$
D)
$$(x,y)\rightarrow(y,x)$$
Answer:
$$(x,y)\rightarrow(-x,-y)$$
Useful Formula for this Question:
Reflection in x-axis
$$(x,y)\rightarrow(x,-y)$$
Reflection in y-axis
$$(x,-y)\rightarrow(-x,-y)$$
Solution:
After reflection in the x-axis,
$$(x,y)\rightarrow(x,-y)$$
Again reflecting in the y-axis,
$$(x,-y)\rightarrow(-x,-y)$$
Therefore, both coordinates change their signs.
Hence, the correct answer is
$$(x,y)\rightarrow(-x,-y)$$
Q3. Which of the following points is equidistant from both coordinate axes but does not lie on either axis?
A)
$$(0,8)$$
B)
$$(-7,7)$$
C)
$$(9,0)$$
D)
$$(5,-3)$$
Answer:
$$(-7,7)$$
Useful Formula for this Question:
A point is equidistant from both coordinate axes if
$$|x|=|y|$$
and
$$x\neq0,;y\neq0$$
Solution:
For
$$(-7,7)$$
$$|x|=|y|=7$$
Also,
$$x\neq0,;y\neq0$$
Therefore, the point is equidistant from both axes and does not lie on either axis.
Hence, the correct answer is
$$(-7,7)$$
Q4. Which one of the following points is 4 units below the x-axis and 7 units to the left of the y-axis?
A)
$$(-7,-4)$$
B)
$$(7,-4)$$
C)
$$(-4,-7)$$
D)
$$(-7,4)$$
Answer:
$$(-7,-4)$$
Useful Formula for this Question:
- Left of y-axis
$$x<0$$
- Below x-axis
$$y<0$$
Solution:
The point is
- 7 units left of the y-axis
$$x=-7$$
4 units below the x-axis
$$y=-4$$
Therefore,
$$(-7,-4)$$
is the required point.
Hence, the correct answer is
$$(-7,-4)$$
Q5. Which of the following statements is always true?
A) Every point in the Second Quadrant is equidistant from both axes.
B) Every point on the x-axis has zero distance from the x-axis.
C) Every point reflected in the y-axis changes both coordinates.
D) Every point in the Fourth Quadrant has equal distances from both axes.
Answer:
Every point on the x-axis has zero distance from the x-axis.
Useful Formula for this Question:
Distance from x-axis
$$=|y|$$
Solution:
Every point on the x-axis has
$$y=0$$
Therefore,
$$|y|=0$$
Hence, its distance from the x-axis is zero.
The remaining statements are incorrect because they are not true for all points.
Hence, the correct answer is:
Every point on the x-axis has zero distance from 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
$$
(x,y)\rightarrow(-x,y)$$
Reflection in Both Axes
$$(x,y)\rightarrow(-x,-y)
$$
Sign Convention
First Quadrant
$$(+,+)$$
Second Quadrant
$$(-,+)$$
Third Quadrant
$$(-,-)$$
Fourth Quadrant
$$(+,-)$$
FAQs
Q. What happens if a point is reflected in both the x-axis and y-axis?
Answer:
Both coordinates change their signs.
$$(x,y)\rightarrow(-x,-y)$$
Q. Can a point be equidistant from both axes without lying on an axis?
Answer:
Yes. Any point satisfying
$$|x|=|y|$$
and having both coordinates non-zero is equidistant from both coordinate axes.
Q. How can you determine whether a point lies to the left of the y-axis?
Answer:
A point lies to the left of the y-axis if its x-coordinate is negative.
$$x<0$$
Common Mistakes Students Make
❌ Confusing “left of the y-axis” with “below the x-axis.”
❌ Forgetting that distance is always positive.
❌ Applying the wrong reflection rule.
❌ Ignoring the quadrant while assigning signs.
❌ Assuming equal distances imply the point lies in the First 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
$$(x,y)\rightarrow(-x,-y)$$
✔ Equal distances from both axes
$$|x|=|y|$$
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions –are prepared according to the latest NCERT syllabus and include advanced, HOTS-based, non-repeated questions. They focus on coordinate reasoning, reflections, quadrant analysis, and logical applications to strengthen conceptual understanding. Regular practice of these MCQs will improve analytical thinking and help students perform confidently in CBSE exams, state board examinations, Olympiads, NTSE foundation, and scholarship tests.
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