KTUYSBeta
Log inSign up

Cheat sheet · JEE Preparation Mathematics

Straight Lines cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Mathematics

Cheat sheet

Class 11 · Chapter 9Straight Lines

Parallel lines: equal slopes. Perpendicular lines: slopes multiply to −1.

1. Slope

m=tan⁡θ=y2−y1x2−x1m = \tan\theta = \dfrac{y_2 - y_1}{x_2 - x_1}
tan⁡ϕ=∣m2−m11+m1m2∣\tan\phi = \left|\dfrac{m_2 - m_1}{1 + m_1m_2}\right|

2. Forms of a Line

FormEquation
Point–slopey−y1=m(x−x1)y - y_1 = m(x - x_1)
Two-pointy−y1=y2−y1x2−x1(x−x1)y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)
Slope–intercepty=mx+cy = mx + c
Interceptxa+yb=1\dfrac xa + \dfrac yb = 1
Normalxcos⁡ω+ysin⁡ω=px\cos\omega + y\sin\omega = p
GeneralAx+By+C=0Ax + By + C = 0, slope −AB-\dfrac AB

3. Distances

d=∣Ax1+By1+C∣A2+B2d = \dfrac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}
d=∣C1−C2∣A2+B2d = \dfrac{|C_1 - C_2|}{\sqrt{A^2 + B^2}} (parallel lines)

4. Key Points

  • Horizontal line: slope 0; vertical: undefined.
  • Collinear points: equal slopes.
  • x-axis: y = 0.
  • Area of triangle can test collinearity.

Remember: Slope | 6 forms | point–line distance

Straight Lines: questions and notes

More JEE Preparation Mathematics cheat sheets

Practise Straight Lines

Sign up free to practise the full chapter. Questions you get wrong come back until you've mastered them.

Start practising free

Free to start · No credit card needed