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Cartesian System Quiz - CBSE Class 9 Mathematics

Free practice quiz: Cartesian System (CBSE Class 9 Mathematics). 20 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 9 Mathematics practice quiz has 20 multiple-choice questions on Cartesian System, and 20 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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Cartesian Plane, Axes and Origin

  • The Cartesian plane is formed by two number lines drawn perpendicular to each other.
  • The horizontal line is the x-axis and the vertical line is the y-axis.
  • The axes meet at the origin O, and they divide the plane into four quadrants.
Origin
\[O(0,\,0)\]

Common mistake: Calling the vertical axis the x-axis. Remember: x-axis is horizontal (left–right), y-axis is vertical (up–down).

Coordinates of a Point

  • A point is written as (x, y). The x-coordinate (abscissa) is its distance from the y-axis.
  • The y-coordinate (ordinate) is its distance from the x-axis. Order matters: x always comes first.
  • A point on the x-axis has y = 0. A point on the y-axis has x = 0.
Point on x-axis
\[(a,\,0)\]
Point on y-axis
\[(0,\,b)\]

Common mistake: Thinking (a, 0) lies on the y-axis. If y is zero, the point sits on the x-axis.

Quadrants and Sign Rules

  • Quadrants are numbered I to IV anticlockwise, starting from the top-right region.
  • The signs of x and y tell you the quadrant. Points on an axis lie in no quadrant.
Quadrant I
\[(+,\,+)\]
Quadrant II
\[(-,\,+)\]
Quadrant III
\[(-,\,-)\]
Quadrant IV
\[(+,\,-)\]

Common mistake: Numbering quadrants clockwise. Quadrant IV is bottom-right, so x is positive and y is negative there.

Reflection in the Axes

  • Reflecting in the x-axis keeps x the same and changes the sign of y.
  • Reflecting in the y-axis keeps y the same and changes the sign of x.
Reflection in x-axis
\[(a,\,b)\rightarrow(a,\,-b)\]
Reflection in y-axis
\[(a,\,b)\rightarrow(-a,\,b)\]

Common mistake: Mixing them up. Reflecting in the x-axis changes the y-coordinate, not the x-coordinate.

Distance, Midpoint and Slope

  • For points P(p, q) and Q(r, s), these formulas give the length, middle point and steepness of PQ.
  • Distance and midpoint are found from differences and averages of the coordinates.
Distance PQ
\[PQ=\sqrt{(r-p)^2+(s-q)^2}\]
Distance from origin
\[OP=\sqrt{p^2+q^2}\]
Midpoint of PQ
\[\left(\frac{p+r}{2},\,\frac{q+s}{2}\right)\]
Slope of PQ
\[m=\frac{s-q}{r-p},\; r\neq p\]

Common mistake: Putting x-difference on top in the slope. Slope is change in y divided by change in x.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is the Cartesian plane?

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    Answer: A. A plane divided by two lines

    The Cartesian plane is a plane defined by two perpendicular axes, the x-axis and the y-axis.

  2. In which quadrant is the point (-3, 4) located?

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    Answer: B. Second quadrant

    Points with negative x-coordinates and positive y-coordinates are located in the second quadrant.

  3. How do the signs of x and y change when moving from the first quadrant to the second quadrant?

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    Answer: A. x becomes negative, y remains positive

    In the second quadrant, x-values are negative while y-values remain positive.

  4. How far is the point (5,5) from the origin in the Cartesian plane?

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    Answer: B. √50 units

    The distance from the origin is calculated using the distance formula, √((5-0)² + (5-0)²) = √50.

  5. What is the reflection of the point (4,5) over the y-axis?

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    Answer: A. (-4,5)

    Reflecting over the y-axis changes the x-coordinate's sign while keeping the y-coordinate unchanged.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What are the axes on a Cartesian plane called?
  2. What is the origin on the Cartesian plane?
  3. What are the coordinates of the origin?
  4. Which quadrant does the point (2, -5) lie in on the Cartesian plane?
  5. What is the x-coordinate of a point?
  6. What is the y-coordinate of a point?
  7. How do the signs of x and y change when moving from the second quadrant to the third quadrant?
  8. What is the general formula for the distance between two points (x1, y1) and (x2, y2) on the Cartesian plane?
  9. What is the midpoint of a line segment connecting the points (0,0) and (4,4) on a Cartesian plane?
  10. Which of the following points lies on the x-axis?
  11. Which of the following points lies on the y-axis?
  12. What is the slope of a line passing through the points (-3, -2) and (3, 4)?
  13. What is the reflection of the point (6,-7) over the x-axis?
  14. If (x, y) is in the third quadrant, what are the signs of x and y?
  15. If (x, y) is in the fourth quadrant, what are the signs of x and y?

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