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Cheat sheet · Class 11 · CBSE · Science 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.

CBSE Class 11 · Mathematics

Cheat sheet

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

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