Knowledge organisers

Coordinate Geometry: CBSE Class 9 Maths knowledge organiser

Everything to know about coordinate geometry on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Origin: The point O(0, 0) where the x-axis and y-axis meet.
Coordinates: (x, y): the distances of a point from the y-axis and the x-axis, with signs.
Quadrant: One of the four regions the axes divide the plane into.

Key formulas

Quadrants I to IV: \((+,+)\), \((-,+)\), \((-,-)\), \((+,-)\); on the \(x\)-axis \(y=0\), on the \(y\)-axis \(x=0\)
Distance	\(AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2};\) \(OP=\sqrt{x^2+y^2}\)
Mid-point	\(\left(\frac{x_1+x_2}2,\ \frac{y_1+y_2}2\right)\)
Parallelogram: diagonals share a mid-point; equidistant point \(P\): \(PA^2=PB^2\)

Worked example

Find the distance between \(A(-1, 3)\) and \(B(5, -5)\).

\(AB = \sqrt{6^2 + (-8)^2} = \sqrt{100} = 10\).

Common mistakes

Writing \((y, x)\) instead of \((x, y)\), or reading the ordinate as the distance from the \(y\)-axis.
Squaring a negative difference wrongly: \((-8)^2 = 64\), not \(-64\).
Stopping at \(\sqrt{52}\) instead of simplifying to \(2\sqrt{13}\), or "simplifying" \(\sqrt{a^2 + b^2}\) to \(a + b\).
Forgetting the second value when an equation such as \((a - 5)^2 = 9\) gives \(a - 5 = \pm 3\).

You should be able to…

Place and read points, name the quadrant and use the distance and mid-point formulas in one step.
Find unknown coordinates from a distance or a mid-point and test triangles for right angles or equal sides.
Write complete answers that classify quadrilaterals and triangles from coordinates, and solve map-style case studies.
Handle equidistance conditions, equilateral triangles and proofs in coordinates.

The printable sheet

Coordinate Geometry knowledge organiser for CBSE Class 9 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Coordinate Geometry knowledge organiser (CBSE Class 9 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 9 Maths topics: Number System · Introduction to Polynomials · Sequences and Progressions · Exploring Algebraic Identities · Linear Equations in Two Variables · Introduction to Euclid's Geometry: Axioms and Postulates · Lines and Angles · Triangles – Congruence Theorems · 4-gons (Quadrilaterals) · Circles · Area and Perimeter · Surface Area and Volume · Statistics · Introduction to Probability · All CBSE Class 9 Maths organisers