CBSE Class 9 Maths — Coordinate Geometry

Chapter Overview & Weightage

Coordinate Geometry in Class 9 is the entry point to one of the most powerful tools in mathematics — the ability to describe geometric shapes using numbers. This chapter lays the foundation for Class 10’s more detailed treatment.

Key Concepts You Must Know

The Cartesian plane: Two perpendicular number lines — the x-axis (horizontal) and y-axis (vertical) — intersect at the origin O = (0, 0).

Coordinates: A point is described by an ordered pair $(x, y)$. The x-coordinate (abscissa) tells horizontal distance from the y-axis; the y-coordinate (ordinate) tells vertical distance from the x-axis.

Four quadrants:

On the axes: A point on the x-axis has $y = 0$. A point on the y-axis has $x = 0$. The origin has both $x = 0$ and $y = 0$.

Mirror image of a point:

• Reflection in x-axis: $(x, y) \to (x, -y)$
• Reflection in y-axis: $(x, y) \to (-x, y)$
• Reflection in origin: $(x, y) \to (-x, -y)$

Plotting Points — The Systematic Method

To plot $(a, b)$:

1. Start at the origin (0, 0)
2. Move $|a|$ units right (if $a > 0$) or left (if $a < 0$) along the x-axis
3. Move $|b|$ units up (if $b > 0$) or down (if $b < 0$) along the y-axis
4. Mark the point with a dot and label it

Solved Previous Year Questions

PYQ 1 (2 marks)

In which quadrant or on which axis do the following points lie? (a) (−5, 7) (b) (3, 0) (c) (−2, −4) (d) (0, −6)

(a) $x < 0$, $y > 0$ → Second Quadrant (b) $y = 0$, $x > 0$ → Positive x-axis (c) $x < 0$, $y < 0$ → Third Quadrant (d) $x = 0$, $y < 0$ → Negative y-axis

PYQ 2 (3 marks)

Plot the following points and verify whether they are collinear (lie on the same straight line): A(1, 1), B(2, 2), C(3, 3).

After plotting, all three points lie on the line $y = x$ (the 45° line through the origin). They are collinear.

Visual check: the points form a straight line. No calculation needed at Class 9 level, but at Class 10 level you would check if the slope between any two pairs is equal: $\frac{2-1}{2-1} = 1$, $\frac{3-2}{3-2} = 1$. Equal slopes confirm collinearity.

PYQ 3 (1 mark)

What is the name of the point where the x-axis and y-axis intersect?

The origin, denoted by O, with coordinates (0, 0).

PYQ 4 (2 marks)

A point lies on the x-axis at a distance of 7 units from the y-axis on the left side. What are its coordinates?

The point is on the x-axis, so $y = 0$. It’s 7 units to the left of the y-axis, so $x = -7$.

Coordinates: $(-7, 0)$.

Difficulty Distribution

Expert Strategy

Keep graph paper ready. Plotting is a hands-on skill. Practice drawing the axes neatly with a ruler, marking equal intervals, and plotting points accurately.

Label everything. In board exams, label the x-axis, y-axis, origin, and each plotted point by name. Missing labels cost marks.

Understand the sign pattern. The sign rule for quadrants (++, −+, −−, +−) follows a simple pattern: I is all positive, and as you go counterclockwise, the x-sign flips first. Visualize the number line in both directions.

Common Traps