What is the difference between abscissa and ordinate in Class 9 Co-ordinate Geometry?

The abscissa is the x-coordinate (the first number in the ordered pair), which gives the horizontal distance and direction from the y-axis. The ordinate is the y-coordinate (the second number), which gives the vertical distance and direction from the x-axis. In the point (4, −8), the abscissa is 4 and the ordinate is −8.

In which quadrant does the point (−2, 3) lie?

The point (−2, 3) lies in the Second Quadrant (Q₂). This is because x = −2 is negative (point is to the left of the y-axis) and y = 3 is positive (point is above the x-axis). Q₂ contains all points with negative x and positive y coordinates.

How do you determine if a point lies on an axis in the Cartesian plane?

A point lies on the x-axis if and only if its y-coordinate (ordinate) is 0, like (3, 0) or (−5, 0). A point lies on the y-axis if and only if its x-coordinate (abscissa) is 0, like (0, 7) or (0, −3). If both coordinates are 0, the point is the origin, which lies on both axes. Points with neither coordinate equal to 0 lie inside a quadrant, not on any axis.

What is the key observation when plotting points with the same y-coordinate or same x-coordinate?

When all plotted points have y = 0, they all lie on the x-axis — confirming that the ordinate of any x-axis point is 0. When all points have x = 0, they all lie on the y-axis — confirming that the abscissa of any y-axis point is 0. More generally, points with the same x-value form a vertical line parallel to the y-axis, and points with the same y-value form a horizontal line parallel to the x-axis.

Exercise 5.2 — Cartesian System | Class 9 Maths | Co-ordinate Geometry

The Cartesian System — Axes, Quadrants, and Key Concepts

Exercise 5.2 is the core of Class 9 Co-ordinate Geometry. It establishes the formal language of the Cartesian plane — the two axes, the four quadrants, and the precise vocabulary (abscissa, ordinate) used to describe the position of every point. Mastering this exercise is essential before you can plot equations or solve geometry problems algebraically.

Essential vocabulary for Exercise 5.2:
◆ x-axis — the horizontal number line (positive to the right, negative to the left).
◆ y-axis — the vertical number line (positive upward, negative downward).
◆ Origin (O) — the intersection point at (0, 0).
◆ Abscissa — the x-coordinate; the first number in the ordered pair.
◆ Ordinate — the y-coordinate; the second number in the ordered pair.
◆ Quadrant — one of the four regions created by the two axes.

Figure 1: The Cartesian plane showing all four quadrants with their sign conventions.

Q₁ — First Quadrant

x > 0, y > 0 → both positive

Q₂ — Second Quadrant

x < 0, y > 0 → x negative, y positive

Q₃ — Third Quadrant

x < 0, y < 0 → both negative

Q₄ — Fourth Quadrant

x > 0, y < 0 → x positive, y negative

Exercise 5.2 — Question 1: Identify the Quadrant

For each point, look at the signs of x and y. A positive x means right of the y-axis; positive y means above the x-axis. If a coordinate is zero, the point lies on an axis, not inside any quadrant.

(i) (−2, 3)

x = −2 < 0 → left side y = 3 > 0 → above x-axis

Ans: Second Quadrant (Q₂)

(ii) (5, −3)

x = 5 > 0 → right side y = −3 < 0 → below x-axis

Ans: Fourth Quadrant (Q₄)

(iii) (4, 2)

x = 4 > 0 → right side y = 2 > 0 → above x-axis

Ans: First Quadrant (Q₁)

(iv) (−7, −6)

x = −7 < 0 → left side y = −6 < 0 → below x-axis

Ans: Third Quadrant (Q₃)

(v) (0, 8)

x = 0 → on the y-axis Not in any quadrant

Ans: On the y-axis

(vi) (3, 0)

y = 0 → on the x-axis Not in any quadrant

Ans: On the x-axis

(vii) (−4, 0)

y = 0 → on the x-axis Not in any quadrant

Ans: On the x-axis

(viii) (0, −6)

x = 0 → on the y-axis Not in any quadrant

Ans: On the y-axis

Exercise 5.2 — Question 2: Abscissa and Ordinate

The abscissa is always the x-coordinate (first number). The ordinate is always the y-coordinate (second number). These two terms are used throughout higher-level mathematics, so knowing them by heart is important.

(i) (4, −8)

First value = abscissa Second value = ordinate

Abscissa: 4 | Ordinate: −8

(ii) (−5, 3)

Abscissa: −5 | Ordinate: 3

(iii) (0, 0)

Origin — both values zero

Abscissa: 0 | Ordinate: 0

(iv) (5, 0)

Point on x-axis

Abscissa: 5 | Ordinate: 0

(v) (0, −8)

Point on y-axis

Abscissa: 0 | Ordinate: −8

Exercise 5.2 — Question 3: Points on Axes

A point lies on the x-axis if and only if its y-coordinate (ordinate) is 0. A point lies on the y-axis if and only if its x-coordinate (abscissa) is 0. If neither coordinate is 0, the point is inside a quadrant and does not lie on any axis.

(i) (−5, −8)

Both coordinates non-zero

Does not lie on any axis

(ii) (0, 13)

x = 0 → on y-axis

Lies on the y-axis

(iii) (4, −2)

Both coordinates non-zero

Does not lie on any axis

(iv) (−2, 0)

y = 0 → on x-axis

Lies on the x-axis

(v) (0, −8)

x = 0 → on y-axis

Lies on the y-axis

(vi) (7, 0)

y = 0 → on x-axis

Lies on the x-axis

(vii) (0, 0)

x = 0 AND y = 0 → origin

Lies on both axes (Origin)

Exercise 5.2 — Question 4: Reading from a Graph

In this question, several named points (L, M, N, Q, R, P) are plotted on a coordinate grid. You must identify their coordinates by reading the x and y values directly from the graph. The dashed reference lines in the figure help you trace each point back to both axes.

(i) Ordinate of L

L is at position (−8, −7) Ordinate = y-coordinate

Ans: −7

(ii) Ordinate of Q

Q is at position (5, 7) Ordinate = y-coordinate

Ans: 7

(iii) Point at (−2, −2)

Find which point has x=−2, y=−2

Ans: Point R

(iv) Point at (5, −4)

Find which point has x=5, y=−4

Ans: Point P

(v) Abscissa of N

N is at position (4, 0) on x-axis Abscissa = x-coordinate

Ans: 4

(vi) Abscissa of L

L is at position (−8, −7) Abscissa = x-coordinate

Ans: −3 (as given in textbook figure)

Exercise 5.2 — Question 5: True or False

Each statement tests a specific rule about the Cartesian plane. For false statements, you must write the corrected version — this skill of identifying and fixing errors is equally important as knowing the correct answer.

(i) The horizontal line in the Cartesian plane is called the Y-axis.

FALSE

✏️ Correction: The horizontal line is called the X-axis.

(ii) The vertical line in the Cartesian plane is called the Y-axis.

TRUE

(iii) The point on both axes is called the origin.

TRUE

ℹ️ The origin (0, 0) is the unique point where the x-axis and y-axis intersect.

(iv) The point (2, −3) lies in the Third Quadrant.

FALSE

✏️ Correction: x = 2 > 0, y = −3 < 0 → lies in Fourth Quadrant (Q₄).

(v) (−5, −8) lies in the Fourth Quadrant.

FALSE

✏️ Correction: x = −5 < 0, y = −8 < 0 → lies in Third Quadrant (Q₃).

(vi) (−x, −y) lies in Q₁ when x < 0 and y < 0.

TRUE

ℹ️ If x < 0, then −x > 0. If y < 0, then −y > 0. Both coordinates positive → Q₁.

Exercise 5.2 — Question 6: Plotting and Observing Patterns

Part (i): Points where y = 0

Plot: (1,0), (3,0), (−2,0), (−5,0), (0,0), (5,0), (−6,0)

Figure 2(i): All points with y = 0 lie on the x-axis (shown in red).

Observation: Every point where y = 0 falls exactly on the x-axis. Conclusion: The ordinate of any point on the x-axis is always 0.

Part (ii): Points where x = 0

Plot: (0,1), (0,3), (0,−2), (0,−5), (0,0), (0,5), (0,−6)

Observation: Every point where x = 0 falls exactly on the y-axis. Conclusion: The abscissa of any point on the y-axis is always 0.

Complete Reference Table — Cartesian Plane Rules

Condition on (x, y)	Location	Sign of x	Sign of y
x > 0, y > 0	First Quadrant Q₁	+	+
x < 0, y > 0	Second Quadrant Q₂	−	+
x < 0, y < 0	Third Quadrant Q₃	−	−
x > 0, y < 0	Fourth Quadrant Q₄	+	−
y = 0 (any x)	On the x-axis	Any	0
x = 0 (any y)	On the y-axis	0	Any
x = 0, y = 0	Origin O	0	0

Distance from a point (x, y) to the x-axis = |y| units (the ordinate's absolute value).
Distance from a point (x, y) to the y-axis = |x| units (the abscissa's absolute value).
Points on an axis are NOT inside any quadrant. Quadrants are the open regions between axes.
The origin (0, 0) lies on both axes simultaneously and belongs to neither quadrant.