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About Coordinate Geometry Introduction — Class 7 CBSE

Plot points on the Cartesian plane and interpret coordinates. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 13). 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

  • Introduction to Coordinate Geometry: Locating Points
  • The Coordinate Plane: X-axis, Y-axis, and Origin
  • Plotting Points and Understanding Coordinates
  • Quadrants: Dividing the Coordinate Plane
  • Summary, Connections, and Practice

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

Coordinate Geometry Introduction — solved examples for Class 7 CBSE

Example 1easy

Which of the following statements correctly describes the x-axis and y-axis in a Cartesian plane?
  1. A)A. The x-axis is a horizontal line, and the y-axis is a vertical line; they intersect at the origin.
  2. B)B. The x-axis is a vertical line, and the y-axis is a horizontal line; they intersect at the origin.
  3. C)C. Both x-axis and y-axis are horizontal lines that never intersect.
  4. D)D. Both x-axis and y-axis are vertical lines that intersect at any point.

Step-by-step solution

  1. The Cartesian plane is formed by two perpendicular number lines: the horizontal x-axis and the vertical y-axis.
  2. These two axes intersect at a point called the origin, which has coordinates (0, 0).
  3. Therefore, the statement that the x-axis is horizontal, the y-axis is vertical, and they intersect at the origin is correct.

Answer: A. The x-axis is a horizontal line, and the y-axis is a vertical line; they intersect at the origin.

Example 2medium

Which of the following statements about the Cartesian plane is TRUE?
  1. A)The x-axis is always vertical.
  2. B)The y-axis is always horizontal.
  3. C)The point where the x-axis and y-axis intersect is called the origin.
  4. D)All points have negative coordinates in the first quadrant.

Step-by-step solution

  1. The x-axis is the horizontal line and the y-axis is the vertical line in the Cartesian plane.
  2. The point where the horizontal x-axis and the vertical y-axis meet is known as the origin, represented by the coordinates (0, 0).
  3. In the first quadrant, both x and y coordinates are positive.

Answer: The point where the x-axis and y-axis intersect is called the origin.

Example 3hard

If point A(x, y) lies in the second quadrant, which quadrant would point B(-x, -y) lie in?
  1. A)First Quadrant
  2. B)Fourth Quadrant
  3. C)Third Quadrant
  4. D)On the Y-axis

Step-by-step solution

  1. In the second quadrant, the x-coordinate is negative (x < 0) and the y-coordinate is positive (y > 0).
  2. For point B(-x, -y), we need to find the signs of its coordinates. Since x < 0, then -x > 0 (positive). Since y > 0, then -y < 0 (negative).
  3. Therefore, point B has a positive x-coordinate and a negative y-coordinate.
  4. A point with a positive x-coordinate and a negative y-coordinate lies in the Fourth Quadrant.

Answer: Fourth Quadrant

Practice questions on Coordinate Geometry Introduction

  1. Q1.easy

    Rani is asked to locate the 'origin' on a coordinate plane. Which of the following points should she mark?
    1. A)A. (1, 0)
    2. B)B. (0, 1)
    3. C)C. (0, 0)
    4. D)D. (1, 1)
    Show answer

    Answer: C. (0, 0)

    Hint: The origin is the starting point where both the x and y axes meet. What are the values at this central meeting point?

  2. Q2.easy

    When we write coordinates as an 'ordered pair' like (3, 5), what does the 'ordered' part signify?
    1. A)A. It means the numbers must always be positive.
    2. B)B. It means the first number always refers to the y-coordinate and the second to the x-coordinate.
    3. C)C. It means the order of the numbers matters; (3, 5) is different from (5, 3).
    4. D)D. It means the numbers must always be whole numbers.
    Show answer

    Answer: C. It means the order of the numbers matters; (3, 5) is different from (5, 3).

    Hint: Consider if swapping the x and y values changes the position of a point on the graph.

  3. Q3.easy

    Ravi wants to plot the point P(4, -2) on a coordinate plane. He first moves 4 units down from the origin and then 2 units to the right. Is his method correct? Why or why not?
    1. A)A. Yes, his method is correct because 4 is positive and -2 is negative.
    2. B)B. No, he should first move 4 units to the right from the origin and then 2 units down.
    3. C)C. No, he should first move 4 units up from the origin and then 2 units left.
    4. D)D. Yes, his method is correct because the order of movement doesn't matter.
    Show answer

    Answer: B. No, he should first move 4 units to the right from the origin and then 2 units down.

    Hint: Remember that the first coordinate is for the x-axis (horizontal movement) and the second is for the y-axis (vertical movement). Positive x is right, negative x is left. Positive y is up, negative y is down.

  4. Q4.medium

    A point P is located on a graph sheet. If you start from the origin, move 5 units to the right along the x-axis, and then 3 units up parallel to the y-axis, you reach point P. What are the coordinates of point P?
    1. A)(3, 5)
    2. B)(5, 3)
    3. C)(0, 5)
    4. D)(3, 0)
    Show answer

    Answer: (5, 3)

    Hint: Remember that the first number in a coordinate pair represents the movement along the x-axis (horizontal), and the second number represents the movement along the y-axis (vertical).

  5. Q5.medium

    For the point (15, 0), what is the ordinate?
    1. A)15
    2. B)(15, 0)
    3. C)1
    4. D)0
    Show answer

    Answer: 0

    Hint: Recall the definitions of abscissa and ordinate. The ordinate is the y-coordinate.

  6. Q6.medium

    To plot the point (4, 0) on a Cartesian plane, you would move 4 units along the _____ axis and 0 units along the _____ axis.
    1. A)x, y
    2. B)y, x
    3. C)x, x
    4. D)y, y
    Show answer

    Answer: x, y

    Hint: The first coordinate corresponds to horizontal movement, and the second coordinate corresponds to vertical movement.

  7. Q7.hard

    Three vertices of a square are A(1, 4), B(1, -2), and C(7, -2). What are the coordinates of the fourth vertex D?
    1. A)(7, 1)
    2. B)(4, 7)
    3. C)(1, 7)
    4. D)(7, 4)
    Show answer

    Answer: (7, 4)

    Hint: Remember the properties of a square: opposite sides are parallel and equal in length, and adjacent sides are perpendicular. Plotting the given points might help visualize the missing vertex.

  8. Q8.hard

    A point P is equidistant from the x-axis and the y-axis. If P lies in the third quadrant and its perpendicular distance from the x-axis is 5 units, what are the coordinates of P?
    1. A)(-5, -5)
    2. B)(5, 5)
    3. C)(-5, 5)
    4. D)(5, -5)
    Show answer

    Answer: (-5, -5)

    Hint: Recall that the distance from the x-axis is the absolute value of the y-coordinate, and the distance from the y-axis is the absolute value of the x-coordinate. Also, remember the signs in the third quadrant.

  9. Q9.hard

    A student claims that a point (0, -3) lies in the third quadrant because its y-coordinate is negative. What is the flaw in this reasoning?
    1. A)The x-coordinate is also negative, which is required for the third quadrant.
    2. B)Points on an axis do not lie in any quadrant.
    3. C)The y-coordinate being negative means it's in the fourth quadrant, not the third.
    4. D)The point (0, -3) actually lies in the second quadrant.
    Show answer

    Answer: Points on an axis do not lie in any quadrant.

    Hint: Consider the definition of a quadrant. Does a point lying *on* an axis satisfy the conditions for being *within* a quadrant?

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