Straight Line formulas

Every formula JEE Advanced expects you to know for Straight Line, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

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Formulas: 32
Subject: Mathematics
Exam: JEE Advanced
No sign-in needed: ₹0

Straight Line, every formula

32 formulas, typeset and free. Print it, or keep it open beside your practice.

Distance between two points
$d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$
Section formula (internal)
$(\frac{m x _{2} + n x _{1}}{m + n}, \frac{m y _{2} + n y _{1}}{m + n})$
Section formula (external)
$(\frac{m x _{2} - n x _{1}}{m - n}, \frac{m y _{2} - n y _{1}}{m - n})$
Midpoint
$(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$
Centroid of a triangle
$(\frac{x _{1} + x _{2} + x _{3}}{3}, \frac{y _{1} + y _{2} + y _{3}}{3})$
Area of a triangle
$\frac{1}{2} ∣ x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}) ∣$
Collinearity
$area = 0$
three points
Slope
$m = tan θ = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}$
Slope-intercept form
$y = m x + c$
Point-slope form
$y - y_{1} = m (x - x_{1})$
Two-point form
$y - y_{1} = \frac{y _{2} - y _{1}}{x _{2} - x _{1}} (x - x_{1})$
Intercept form
$\frac{x}{a} + \frac{y}{b} = 1$
Normal form
$x cos α + y sin α = p$
p = distance from origin
Slope from general form
$a x + b y + c = 0 \Rightarrow m = - \frac{a}{b}$
Angle between two lines
$tan θ = \frac{m _{1} - m _{2}}{1 + m _{1} m _{2}}$
Parallel lines
$m_{1} = m_{2}$
Perpendicular lines
$m_{1} m_{2} = - 1$
Distance point to line
$\frac{∣ a x _{1} + b y _{1} + c ∣}{a ^{2} + b ^{2}}$
Distance between parallel lines
$\frac{∣ c _{1} - c _{2} ∣}{a ^{2} + b ^{2}}$
Perpendicular distance from origin
$\frac{∣ c ∣}{a ^{2} + b ^{2}}$
Line parallel to ax+by+c=0
$a x + b y + k = 0$
Line perpendicular to ax+by+c=0
$b x - a y + k = 0$
Family of lines through intersection
$L_{1} + λ L_{2} = 0$
Concurrency of three lines
$a_{1} a_{2} a_{3} b_{1} b_{2} b_{3} c_{1} c_{2} c_{3} = 0$
Position of two points w.r.t. a line
$(a x_{1} + b y_{1} + c) (a x_{2} + b y_{2} + c) > 0 same side$
Angle bisectors
$\frac{a _{1} x + b _{1} y + c _{1}}{a _{1}^{2} + b _{1}^{2}} = \pm \frac{a _{2} x + b _{2} y + c _{2}}{a _{2}^{2} + b _{2}^{2}}$
Foot of perpendicular
$\frac{x - x _{1}}{a} = \frac{y - y _{1}}{b} = - \frac{a x _{1} + b y _{1} + c}{a ^{2} + b ^{2}}$
Image of a point in a line
$\frac{x - x _{1}}{a} = \frac{y - y _{1}}{b} = - \frac{2 ( a x _{1} + b y _{1} + c )}{a ^{2} + b ^{2}}$
Distance (parametric) form
$\frac{x - x _{1}}{cos θ} = \frac{y - y _{1}}{sin θ} = r$
Slope of line through origin at angle θ
$y = x tan θ$
Line making equal intercepts
$x + y = a$
Reflection of x-axis line slope
$slope of tangent \to - slope for reflection in x-axis$

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Straight Line formulas

Straight Line, every formula

Distance between two points

Section formula (internal)

Section formula (external)

Midpoint

Centroid of a triangle

Area of a triangle

Collinearity

Slope

Slope-intercept form

Point-slope form

Two-point form

Intercept form

Normal form

Slope from general form

Angle between two lines

Parallel lines

Perpendicular lines

Distance point to line

Distance between parallel lines

Perpendicular distance from origin

Line parallel to ax+by+c=0

Line perpendicular to ax+by+c=0

Family of lines through intersection

Concurrency of three lines

Position of two points w.r.t. a line

Angle bisectors

Foot of perpendicular

Image of a point in a line

Distance (parametric) form

Slope of line through origin at angle θ

Line making equal intercepts

Reflection of x-axis line slope

More JEE Advanced Mathematics formula sheets

Know the Straight Line formulas. Now use them.

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