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Practice Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers based on the latest NCERT syllabus. Solve higher-level 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: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
The chapter Coordinate Geometry introduces students to representing points on the Cartesian plane using ordered pairs. Besides plotting points and identifying quadrants, students learn to solve logical problems involving distances from coordinate axes, reflections, and coordinate relationships. A strong understanding of this chapter is essential for advanced mathematics and graph-based concepts.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Ordered Pairs
✔ Coordinate Axes
✔ Distance from Coordinate Axes
✔ Reflection of Points
✔ Quadrants and Sign Convention
✔ Logical Coordinate Problems
✔ NCERT & Board Exam Concepts
Why This Topic Is Important?
Coordinate Geometry develops logical thinking and graphical interpretation skills. It serves as the basis for graphing, transformations, and analytical geometry, making it one of the most important foundation chapters in Mathematics.
Exam Relevance
These questions are useful for:
✔ CBSE School Exams
✔ State Board Exams
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Olympiad & Scholarship Exams
Q1. A point is 6 units from the x-axis and 8 units from the y-axis. Which of the following points satisfies these conditions?
A)
$$(8,6)$$
B)
$$(-8,6)$$
C)
$$(8,-6)$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
Distance from x-axis
$$=|y|$$
Distance from y-axis
$$=|x|$$
Solution:
The point is
- 6 units from the x-axis
$$|y|=6$$
- 8 units from the y-axis
$$|x|=8
Possible points are
$$(8,6),;(-8,6),;(8,-6),;(-8,-6)$$
Among the given options, A, B, and C satisfy the conditions.
Hence, the correct answer is:
All of these
Q2. The reflection of the point
$$(-9,4)$$
in the x-axis is:
A)
$$(9,4)$$
B)
$$(-9,-4)$$
C)
$$(9,-4)$$
D)
$$(-4,9)$$
Answer:
$$(-9,-4)$$
Useful Formula for this Question:
Reflection in x-axis:
$$(x,y)\rightarrow(x,-y)$$
Solution:
Only the sign of the y-coordinate changes.
Therefore,
$$(-9,4)\rightarrow(-9,-4)$$
Hence, the correct answer is
$$(-9,-4)$$
Q3. Which of the following points is not equidistant from the coordinate axes?
A)
$$(7,7)$$
B)
$$(-5,5)$$
C)
$$(-9,-9)$$
D)
$$(6,-8)$$
Answer:
$$(6,-8)$$
Useful Formula for this Question:
A point is equidistant from both axes if
$$|x|=|y|$$
Solution:
For
$$(6,-8)$$
$$|6|\ne|8|$$
Therefore, the distances from the two axes are different.
Hence, the correct answer is
$$(6,-8)$$
Q4. If a point lies in the Fourth Quadrant and is 5 units away from the y-axis and 9 units away from the x-axis, then the point is:
A)
$$(5,-9)$$
B)
$$(-5,9)$$
C)
$$(-5,-9)$$
D)
$$(5,9)$$
Answer:
$$(5,-9)$$
Useful Formula for this Question:
Fourth Quadrant:
$$(+,-)$$
Distance from y-axis
$$=|x|$$
Distance from x-axis
$$=|y|$$
Solution:
Since the point lies in the Fourth Quadrant,
- x-coordinate is positive.
- y-coordinate is negative.
Distance from y-axis
$$=5$$
Therefore,
$$x=5$$
Distance from x-axis
$$=9$$
Therefore,
$$y=-9$$
Hence, the point is
$$(5,-9)$$
Q5. Which one of the following statements is always true?
A) Reflection in the y-axis changes only the y-coordinate.
B) Reflection in the x-axis changes only the x-coordinate.
C) Reflection in the y-axis changes only the sign of the x-coordinate.
D) Reflection in the x-axis changes both coordinates.
Answer:
Reflection in the y-axis changes only the sign of the x-coordinate.
Useful Formula for this Question:
Reflection in y-axis
$$(x,y)\rightarrow(-x,y)$$
Solution:
During reflection in the y-axis,
- x-coordinate changes its sign.
- y-coordinate remains unchanged.
Therefore,
$$(x,y)\rightarrow(-x,y)$$
Hence, the correct answer is:
Reflection in the y-axis changes only the sign of the x-coordinate.
Important Formulas and Concepts
Ordered Pair
$$(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)$$
Quadrant Sign Convention
First Quadrant
$$(+,+)$$
Second Quadrant
$$(-,+)$$
Third Quadrant
$$(-,-)$$
Fourth Quadrant
$$(+,-)$$
FAQs
Q. How can you determine whether a point is equidistant from both axes?
Answer:
Compare the absolute values of the coordinates.
If
$$|x|=|y|$$
then the point is equidistant from both coordinate axes.
Q. What happens to a point after reflection in the x-axis?
Answer:
The x-coordinate remains the same, while the sign of the y-coordinate changes.
$$(x,y)\rightarrow(x,-y)$$
Q. Can more than one point have the same distance from the coordinate axes?
Answer:
Yes. Different points can have the same absolute values of x and y while lying in different quadrants.
Common Mistakes Students Make
❌ Forgetting to use absolute values while finding distances.
❌ Choosing the wrong sign according to the quadrant.
❌ Confusing reflection in the x-axis with reflection in the y-axis.
❌ Ignoring the quadrant while determining coordinates.
❌ Assuming distance from an axis can be negative.
Quick Revision Notes
✔ Distance from x-axis
$$=|y|$$
✔ Distance from y-axis
$$=|x|$$
✔ Reflection in x-axis
$$(x,y)\rightarrow(x,-y)$$
✔ Reflection in y-axis
$$(x,y)\rightarrow(-x,y)$$
✔ Quadrant sign pattern:
- First → (+,+)
- Second → (-,+)
- Third → (-,-)
- Fourth → (+,-)
✔ Distance is always positive.
Conclusion:
These Class 9 Maths Chapter 3 Coordinate Geometry MCQ Questions with Answers and Solutions – Practice Set 10 are prepared according to the latest NCERT syllabus and include fresh, non-repeated, moderate-to-difficult questions. The questions focus on conceptual understanding, logical reasoning, reflections, coordinate distances, and quadrant analysis. Regular practice of these MCQs will help students improve accuracy, strengthen analytical skills, and score higher in CBSE exams, state board examinations, school tests, Olympiads, and scholarship exams.
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