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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 Cartesian plane 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:
Coordinate Geometry helps students represent geometric figures using numbers and graphs. By understanding ordered pairs, coordinate axes, quadrants, and reflections, students develop strong analytical and visualization skills. These concepts are essential for higher mathematics, graphing, and practical applications in science and engineering.
What You Will Learn?
✔ Cartesian Coordinate System
✔ Coordinates of Points
✔ Distance from Coordinate Axes
✔ Reflection of Points
✔ Identification of Quadrants
✔ Sign Convention
✔ Coordinate-Based Reasoning
✔ Board Exam Concepts
Why This Topic Is Important?
This chapter builds the foundation for analytical geometry, graph plotting, linear equations, and transformations. Questions based on coordinate geometry frequently test conceptual understanding rather than direct memorization, making practice extremely important.
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 4 units away from the y-axis and 7 units above the x-axis. Which of the following points satisfies these conditions?
A)
$$(4,7)$$
B)
$$(-4,7)$$
C)
$$(4,-7)$$
D) Both
$$(4,7)\text{ and }(-4,7)$$
Answer:
Both
$$(4,7)\text{ and }(-4,7)$$
Useful Formula for this Question:
Distance from the y-axis
$$=|x|$$
Distance from the x-axis
$$=|y|$$
Solution:
Distance from the y-axis is
$$4$$
Therefore,
$$x=\pm4$$
The point is 7 units above the x-axis, so
$$y=7$$
Possible points are
$$(4,7)\text{ and }(-4,7)$$
Hence, the correct answer is:
Both
$$(4,7)\text{ and }(-4,7)$$
Q2. If the point
$$(6,-9)$$
is reflected in the x-axis, the image is:
A)
$$(-6,-9)$$
B)
$$(6,9)$$
C)
$$(-6,9)$$
D)
$$(9,6)$$
Answer:
$$(6,9)$$
Useful Formula for this Question:
Reflection in the x-axis:
$$(x,y)\rightarrow(x,-y)$$
Solution:
The given point is
$$(6,-9)$$
Reflection in the x-axis changes only the sign of the y-coordinate.
Therefore,
$$(6,-9)\rightarrow(6,9)$$
Hence, the correct answer is
$$(6,9)$$
Q3. Which of the following points is equidistant from both coordinate axes and lies in the Third Quadrant?
A)
$$(8,-8)$$
B)
$$(-5,-5)$$
C)
$$(-7,7)$$
D)
$$(6,6)$$
Answer:
$$(-5,-5)$$
Useful Formula for this Question:
A point is equidistant from both axes if
$$|x|=|y|$$
Solution:
For
$$(-5,-5)$$
$$|x|=5,\quad |y|=5$$
Both distances are equal, and both coordinates are negative.
Therefore, the point lies in the Third Quadrant.
Hence, the correct answer is
$$(-5,-5)$$
Q4. Which statement is always true for every point lying in the Second Quadrant?
A)
$$x>0,;y>0$$
B)
$$x>0,;y<0$$
C)
$$x<0,;y>0$$
D)
$$x<0,;y<0$$
Answer:
$$x<0,;y>0$$
Useful Formula for this Question:
Second Quadrant
$$(-,+)$$
Solution:
Every point in the Second Quadrant has
- Negative x-coordinate
- Positive y-coordinate
Therefore,
$$x<0,;y>0$$
Hence, the correct answer is
$$x<0,;y>0$$
Q5. The point
$$(-8,-11)$$
is reflected in the y-axis. In which quadrant will the reflected point lie?
A) First Quadrant
B) Second Quadrant
C) Third Quadrant
D) Fourth Quadrant
Answer:
Fourth Quadrant
Useful Formula for this Question:
Reflection in the y-axis:
$$(x,y)\rightarrow(-x,y)$$
Solution:
The point
$$(-8,-11)$$
after reflection becomes
$$(8,-11)$$
The reflected point has
- Positive x-coordinate
- Negative y-coordinate
Therefore, it lies in the Fourth Quadrant.
Hence, the correct answer is:
Fourth Quadrant
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 do you determine the distance of a point from the y-axis?
Answer:
The distance of a point from the y-axis is the absolute value of its x-coordinate.
$$|x|$$
Q. Does reflection in the x-axis change the x-coordinate?
Answer:
No. Reflection in the x-axis changes only the sign of the y-coordinate.
$$(x,y)\rightarrow(x,-y)$$
Q. Which quadrant contains points with negative x-coordinate and positive y-coordinate?
Answer:
The Second Quadrant contains all such points.
$$(-,+)$$
Common Mistakes Students Make
❌ Forgetting that distance is always taken as a positive value.
❌ Confusing reflection in the x-axis with reflection in the y-axis.
❌ Identifying the wrong quadrant after reflection.
❌ Ignoring absolute values while calculating distances.
❌ Assuming points on the axes belong to quadrants.
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 signs:
- First → (+,+)
- Second → (-,+)
- Third → (-,-)
- Fourth → (+,-)
✔ Origin
$$(0,0)$$
Related Links
- Class 9 Maths Chapter 3 Coordinate Geometry part-8
- Class 9 Maths Chapter 3 Coordinate Geometry part-7
- Class 9 Maths Chapter 3 Coordinate Geometry part-6
- Class 9 Maths Chapter 3 Coordinate Geometry part-5
- Class 9 Maths Chapter 3 Coordinate Geometry part-4
- Class 9 Maths Chapter 3 Coordinate Geometry part-3
- Class 9 Maths Chapter 3 Coordinate Geometry part-2
- Class 9 Maths Chapter 3 Coordinate Geometry part-1
- Class 9 Maths Chapter 2 Polynomials part 11
- Class9 Maths Chapter2 Polynomials part 10
- Class 9 Maths Chapter 1 Number Systems, irrational numbers
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