Knowledge organisers

Coordinate Geometry: CBSE Class 10 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

Distance formula: The length between two points, from Pythagoras.
Section formula: Gives the point that divides a line segment in a given ratio m : n.
Mid-point: The point halfway along a segment: the average of the coordinates.

Key formulas

Distance	\(PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2};\) \(OP=\sqrt{x^2+y^2}\)
Section formula, ratio \(m:n\) (internal)	\(\left(\frac{mx_2+nx_1}{m+n},\ \frac{my_2+ny_1}{m+n}\right)\)
Midpoint	\(\left(\frac{x_1+x_2}2,\ \frac{y_1+y_2}2\right)\)
Ratio in which a line or axis divides \(AB\): take \(k:1\) and solve for \(k\)

Worked example

Distance between \((2, -1)\) and \((-4, 7)\): \(\sqrt{36 + 64} = 10\).

Common mistakes

Swapping \(m_1\) and \(m_2\) in the section formula — \(m_1\) multiplies the coordinates of the second point.
Forgetting the square root, or squaring a negative difference incorrectly.
Concluding “square” from equal sides alone (a rhombus also has equal sides); check the diagonals.
Leaving the final distance unsimplified (\(\sqrt{72} = 6\sqrt2\)).

You should be able to…

Find the distance between two points and the mid-point of a segment without slips.
Use the section formula both ways: to find the dividing point and to find the ratio (or an unknown coordinate).
Prove the type of a quadrilateral or triangle from coordinates in a full, reasoned long answer.
Handle trisection points, points equidistant from three given points and right-angle conditions.

The printable sheet

Coordinate Geometry knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Coordinate Geometry knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Arithmetic Progressions · Triangles · Introduction to Trigonometry · Some Applications of Trigonometry · Circles · Areas Related to Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers