Chapter 13 · Class 7 CBSE · MCQ Test
Coordinate Geometry Introduction MCQ Test — Class 7 CBSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Coordinate Geometry Introduction — MCQ Questions
1Which of the following statements correctly describes the x-axis and y-axis in a Cartesian plane?
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Answer: A. The x-axis is a horizontal line, and the y-axis is a vertical line; they intersect at the origin.
Hint: Recall how the coordinate plane is set up. Think about the directions of the two main lines.
Solution:
The Cartesian plane is formed by two perpendicular number lines: the horizontal x-axis and the vertical y-axis.
These two axes intersect at a point called the origin, which has coordinates (0, 0).
Therefore, the statement that the x-axis is horizontal, the y-axis is vertical, and they intersect at the origin is correct.
2Rani is asked to locate the 'origin' on a coordinate plane. Which of the following points should she mark?
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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?
Solution:
The origin is the point where the x-axis and the y-axis intersect.
At this intersection point, the value on the x-axis is 0, and the value on the y-axis is 0.
Thus, the coordinates of the origin are (0, 0).
3When we write coordinates as an 'ordered pair' like (3, 5), what does the 'ordered' part signify?
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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.
Solution:
In an ordered pair (x, y), the first number (x) always represents the position along the x-axis, and the second number (y) always represents the position along the y-axis.
If you swap the order, for example, (3, 5) versus (5, 3), these represent two completely different points on the coordinate plane.
Therefore, 'ordered' signifies that the sequence of numbers is crucial for defining the point's unique location.
4Ravi 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?
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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.
Solution:
For a point (x, y), the x-coordinate indicates horizontal movement from the origin, and the y-coordinate indicates vertical movement.
A positive x-coordinate (like 4) means moving 4 units to the right. A negative y-coordinate (like -2) means moving 2 units down.
Ravi incorrectly started by moving down (y-axis) and then right (x-axis), and also assigned the negative sign to the wrong coordinate during his movement description.
The correct method is to move 4 units right (for x=4) and then 2 units down (for y=-2).
5Imagine a point 'M' is located 5 units to the left of the y-axis and 3 units above the x-axis. What are the coordinates of point M?
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Answer: B. (-5, 3)
Hint: Movement to the left corresponds to negative x-values, and movement above corresponds to positive y-values.
Solution:
The x-coordinate describes the horizontal position relative to the y-axis. '5 units to the left of the y-axis' means x = -5.
The y-coordinate describes the vertical position relative to the x-axis. '3 units above the x-axis' means y = 3.
Combining these, the coordinates of point M are (-5, 3).
6In which quadrant would the point (-6, 2) lie?
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Answer: B. Quadrant II
Hint: Recall the signs of the x and y coordinates in each of the four quadrants.
Solution:
Quadrant I has positive x and positive y coordinates (+, +).
Quadrant II has negative x and positive y coordinates (-, +).
Quadrant III has negative x and negative y coordinates (-, -).
Quadrant IV has positive x and negative y coordinates (+, -).
Since the point (-6, 2) has a negative x-coordinate (-6) and a positive y-coordinate (2), it lies in Quadrant II.
7Which of the following statements is TRUE about points lying on the x-axis?
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Answer: B. All points on the x-axis have their y-coordinate equal to 0.
Hint: Think about what it means for a point to be 'on' the x-axis. What is its vertical position?
Solution:
The x-axis is the horizontal number line. Any point on this line has moved horizontally from the origin but has not moved up or down.
Therefore, the vertical distance from the origin (which is the y-coordinate) for any point on the x-axis must be 0.
Examples include (2, 0), (-5, 0), (0, 0).
8A point R is located on the y-axis, 7 units below the origin. What are the coordinates of point R?
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Answer: C. (0, -7)
Hint: Points on the y-axis have a specific x-coordinate value. 'Below the origin' implies a negative y-coordinate.
Solution:
If a point lies on the y-axis, its x-coordinate must be 0, as it has no horizontal displacement from the origin.
'7 units below the origin' indicates a negative value for the y-coordinate, specifically -7.
Combining these, the coordinates of point R are (0, -7).
9Consider two points: P(1, 4) and Q(4, 1). Which of the following statements is true regarding their positions on a coordinate plane?
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Answer: C. Points P and Q are different points, both located in Quadrant I.
Hint: Remember the concept of ordered pairs. Also, check the signs of coordinates for quadrant identification.
Solution:
For point P(1, 4), both x (1) and y (4) are positive, so it lies in Quadrant I.
For point Q(4, 1), both x (4) and y (1) are also positive, so it also lies in Quadrant I.
Since the order in an ordered pair matters, (1, 4) and (4, 1) represent distinct locations on the plane, even though both are in Quadrant I.
10A student is using a map of their school where the main gate is at the origin (0, 0). The library is located 3 blocks east and 5 blocks north from the main gate. What are the coordinates of the library?
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Answer: D. (3, 5)
Hint: Think of 'east' as positive movement along the x-axis and 'north' as positive movement along the y-axis.
Solution:
Movement 'east' corresponds to a positive change in the x-coordinate. So, 3 blocks east means x = 3.
Movement 'north' corresponds to a positive change in the y-coordinate. So, 5 blocks north means y = 5.
Therefore, the coordinates of the library are (3, 5).
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Tips for Coordinate Geometry Introduction MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Coordinate Geometry Introduction MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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