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09Class 11 Maths

Straight Lines formulas

Slope, line forms and distance formulas for Straight Lines. Picking the right form of the line is usually most of the work.

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All Maths formulas

Basics

Distance between points
d=(x2−x1)2+(y2−y1)2\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Section formula
(mx2+nx1m+n,  my2+ny1m+n)\displaystyle \left(\frac{mx_2 + nx_1}{m + n},\; \frac{my_2 + ny_1}{m + n}\right)

Internal division in ratio m : n.

Slope
m=tan⁡θ=y2−y1x2−x1\displaystyle m = \tan\theta = \frac{y_2 - y_1}{x_2 - x_1}
Angle between lines
tan⁡θ=∣m2−m11+m1m2∣\displaystyle \tan\theta = \left|\frac{m_2 - m_1}{1 + m_1m_2}\right|
Parallel and perpendicular
m1=m2,m1m2=−1\displaystyle m_1 = m_2, \quad m_1m_2 = -1

Forms of a line

Point-slope
y−y1=m(x−x1)\displaystyle y - y_1 = m(x - x_1)
Slope-intercept
y=mx+c\displaystyle y = mx + c
Two-point
y−y1=y2−y1x2−x1(x−x1)\displaystyle y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)
Intercept
xa+yb=1\displaystyle \frac{x}{a} + \frac{y}{b} = 1
Normal
xcos⁡ω+ysin⁡ω=p\displaystyle x\cos\omega + y\sin\omega = p

Distances

Point to line
d=∣Ax1+By1+C∣A2+B2\displaystyle d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}
Between parallel lines
d=∣C1−C2∣A2+B2\displaystyle d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}

A and B must match in both lines.

Where students slip up

  • Applying m₁m₂ = −1 to a vertical line, whose slope is undefined.
  • Using the parallel-line distance before making the x and y coefficients match.

Try it on your weakest chapter.

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