How many practice questions are available for Coordinate Geometry?

SparkEd Math offers 60+ practice questions for Coordinate Geometry across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Coordinate Geometry content free on SparkEd Math?

Yes! All Coordinate Geometry content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Coordinate Geometry differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Coordinate Geometry problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Coordinate Geometry content aligned with the CBSE syllabus?

Yes, all Coordinate Geometry questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Coordinate Geometry — Class 9 CBSE (2025-26)

About Coordinate Geometry — Class 9 CBSE

Plot points on the Cartesian plane and understand abscissa, ordinate, and quadrants. This topic is part of the CBSE Class 9 mathematics syllabus (chapter: Chapter 3). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Coordinate Geometry

Introduction to Coordinate Geometry: The Cartesian Plane
Coordinates of a Point and Quadrants
Plotting Points on the Cartesian Plane
Distances from Axes and Simple Geometric Figures
Summary, Connections, and Preparation for Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

Coordinate Geometry — solved examples for Class 9 CBSE

Example 1easy

In the Cartesian plane, the x-coordinate of a point is also known as its _____, and the y-coordinate is known as its ____.

A)A) ordinate, abscissa
B)B) abscissa, ordinate
C)C) quadrant, axis
D)D) origin, plane

Step-by-step solution

The x-coordinate of a point refers to its horizontal position and is formally called the abscissa.
The y-coordinate of a point refers to its vertical position and is formally called the ordinate.
Therefore, the x-coordinate is the abscissa, and the y-coordinate is the ordinate.

Answer: B) abscissa, ordinate

Example 2medium

For a point P(-7, 10), which of the following statements is true?

A)Its abscissa is 10.
B)Its ordinate is -7.
C)It lies in the Third Quadrant.
D)Its distance from the Y-axis is 7 units.

Step-by-step solution

For P(-7, 10), the x-coordinate (abscissa) is -7 and the y-coordinate (ordinate) is 10. Thus, options A and B are false.
A point with a negative x-coordinate and a positive y-coordinate (-,+) lies in the Second Quadrant, not the Third. So option C is false.
The distance of a point (x, y) from the Y-axis is given by the absolute value of its x-coordinate, |x|. For P(-7, 10), the distance from the Y-axis is |-7| = 7 units. So option D is true.

Answer: Its distance from the Y-axis is 7 units.

Example 3hard

A point P lies in the third quadrant. Its perpendicular distance from the y-axis is three times its perpendicular distance from the x-axis. If the sum of the absolute values of its coordinates is 16, which of the following could be the coordinates of P?

A)A) (-4, -12)
B)B) (-12, -4)
C)C) (-8, -8)
D)D) (-6, -10)

Step-by-step solution

Let the coordinates of point P be (x, y). Since P lies in the third quadrant, both x and y are negative.
The perpendicular distance from the y-axis is |x|, and from the x-axis is |y|. Given |x| = 3|y|.
Also, the sum of the absolute values of its coordinates is 16, so |x| + |y| = 16.
Substitute |x| = 3|y| into the second equation: 3|y| + |y| = 16, which simplifies to 4|y| = 16. Thus, |y| = 4.
Now find |x|: |x| = 3 × 4 = 12. Since P is in the third quadrant, x = -12 and y = -4. So, P is (-12, -4).

Answer: B) (-12, -4)

Practice questions on Coordinate Geometry

Q1.easy
Which of the following statements correctly describes the signs of the coordinates of a point located in the third quadrant?
1. A)A) x-coordinate is positive, y-coordinate is positive
2. B)B) x-coordinate is negative, y-coordinate is positive
3. C)C) x-coordinate is negative, y-coordinate is negative
4. D)D) x-coordinate is positive, y-coordinate is negative
Show answer
Answer: C) x-coordinate is negative, y-coordinate is negative
Hint: Visualize the Cartesian plane. The third quadrant is below the x-axis and to the left of the y-axis.
Q2.easy
A point P is located 3 units to the left of the y-axis and 4 units above the x-axis. What are the coordinates of point P?
1. A)A) (-3, 4)
2. B)B) (3, -4)
3. C)C) (4, -3)
4. D)D) (-4, 3)
Show answer
Answer: A) (-3, 4)
Hint: "Left of y-axis" indicates negative x, and "above x-axis" indicates positive y.
Q3.easy
Rahul plotted a point M(0, -7) and stated that it lies on the x-axis. Identify the mistake in Rahul's statement.
1. A)A) The point should have been (0, 7) to lie on the x-axis.
2. B)B) The point M(0, -7) actually lies on the y-axis.
3. C)C) A point with a negative coordinate cannot lie on an axis.
4. D)D) The point M(0, -7) lies in the fourth quadrant.
Show answer
Answer: B) The point M(0, -7) actually lies on the y-axis.
Hint: Remember what defines a point lying on the x-axis versus the y-axis. What is always zero for points on the x-axis? What is always zero for points on the y-axis?
Q4.medium
A point has an x-coordinate of 5 and a y-coordinate of -3. In which quadrant does it lie?
1. A)First Quadrant
2. B)Second Quadrant
3. C)Third Quadrant
4. D)Fourth Quadrant
Show answer
Answer: Fourth Quadrant
Hint: Recall the sign conventions for x and y coordinates in each of the four quadrants.
Q5.medium
Which of the following points lies on the Y-axis?
1. A)(4, 0)
2. B)(0, 7)
3. C)(-3, 2)
4. D)(5, 5)
Show answer
Answer: (0, 7)
Hint: Points on the Y-axis always have a specific value for their x-coordinate.
Q6.medium
A point P has coordinates (a, b). If its distance from the X-axis is 6 units and its distance from the Y-axis is 4 units, and it lies in the second quadrant, what are the coordinates of P?
1. A)(4, 6)
2. B)(-4, 6)
3. C)(6, -4)
4. D)(-6, 4)
Show answer
Answer: (-4, 6)
Hint: The distance of a point (x, y) from the X-axis is |y| and from the Y-axis is |x|. Also, remember the sign conventions for coordinates in the second quadrant.
Q7.hard
Three vertices of a parallelogram ABCD are A(2, 3), B(8, 3), and C(10, 7). Find the coordinates of the fourth vertex D.
1. A)A) (4, 7)
2. B)B) (6, 7)
3. C)C) (4, 1)
4. D)D) (2, 7)
Show answer
Answer: A) (4, 7)
Hint: Recall the property of parallelograms that their diagonals bisect each other. This means the midpoint of diagonal AC must be the same as the midpoint of diagonal BD.
Q8.hard
Three vertices of a triangle are A(2, 1), B(10, 1), and C(6, 7). What is the area of triangle ABC?
1. A)A) 18 sq. units
2. B)B) 20 sq. units
3. C)C) 22 sq. units
4. D)D) 24 sq. units
Show answer
Answer: D) 24 sq. units
Hint: Look for a side of the triangle that is parallel to one of the coordinate axes. This will simplify calculating the base and height.
Q9.hard
If points P(a, b), Q(c, d), and R(e, f) are collinear and lie on a line parallel to the y-axis, which of the following statements must be true?
1. A)A) a + b + c = 0
2. B)B) b = d = f
3. C)C) a = c = e
4. D)D) The points form a horizontal line.
Show answer
Answer: C) a = c = e
Hint: Consider the characteristics of a line that is parallel to the y-axis. What do all points on such a line have in common?

These are 9 of the 60 questions available for Coordinate Geometry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.