Knowledge organisers

Straight Lines: CBSE Class 11 Maths knowledge organiser

Everything to know about straight lines 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

Slope: m = tan θ, the steepness of a line; m = (y₂ − y₁)/(x₂ − x₁).
Intercept: Where a line crosses an axis.
Perpendicular distance: The shortest distance from a point to a line.

Key formulas

Slope; angle between	\(m=\tan\theta=\frac{y_2-y_1}{x_2-x_1};\) \(\tan\phi=\left\|\frac{m_2-m_1}{1+m_1m_2}\right\|\)
Parallel \(m_1=m_2\); perpendicular \(m_1m_2=-1\)	\(y-y_1=m(x-x_1),\) \(y=mx+c,\) \(\frac xa+\frac yb=1\)
Point to line	\(\frac{\|Ax_1+By_1+C\|}{\sqrt{A^2+B^2}}\)
Parallel lines \(Ax+By+C_1=0\), \(Ax+By+C_2=0\) (same \(A, B\))	\(\frac{\|C_1-C_2\|}{\sqrt{A^2+B^2}}\)

Worked example

Find the equation of the line through \((2, -1)\) parallel to \(3x - y + 4 = 0\).

Slope \(3\): \(y + 1 = 3(x - 2)\), i.e. \(3x - y - 7 = 0\).

Common mistakes

Slope written as \(\dfrac{x_2 - x_1}{y_2 - y_1}\), or with the points in a different order on top and bottom.
Forgetting the modulus in the angle and distance formulae.
Distance between parallel lines without first making the coefficients of \(x\) and \(y\) the same.
Slope of \(Ax + By + C = 0\) taken as \(\dfrac AB\) instead of \(-\dfrac AB\).

You should be able to…

Find slopes, test parallel and perpendicular lines and write simple line equations.
Use every form of the line equation, test collinearity and find distances from a point to a line.
Combine line equations, distances and areas in triangle problems.
Find lines at a given angle, reflections of points and distances between parallel lines.

The printable sheet

Straight Lines knowledge organiser for CBSE Class 11 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Straight Lines knowledge organiser (CBSE Class 11 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 11 Maths topics: Sets · Relations and Functions · Trigonometric Functions · Complex Numbers and Quadratic Equations · Linear Inequalities · Permutations and Combinations · Binomial Theorem · Sequences and Series · Conic Sections · Introduction to Three Dimensional Geometry · Limits and Derivatives · Statistics · Probability · All CBSE Class 11 Maths organisers