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Straight Lines formula sheet

Every formula in the Straight Lines chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 24 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Coordinates, section formula and area

Distance and section formula
10× asked, last 2025
AB=(x2−x1)2+(y2−y1)2P=(mx2+nx1m+n, my2+ny1m+n)\begin{aligned}&AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\&P=\left(\frac{mx_2+nx_1}{m+n},\ \frac{my_2+ny_1}{m+n}\right)\end{aligned}
AP:PB=m:nAP:PB=m:n; weight mm on the far end BB. External: n→−nn\to-n.
Parallelogram and midpoints
8× asked, last 2026
A+C=B+D  (parallelogram ABCD)A=E+F−D  (from midpoints)\begin{aligned}&A+C=B+D\ \ (\text{parallelogram }ABCD)\\&A=E+F-D\ \ (\text{from midpoints})\end{aligned}
D,E,FD,E,F: midpoints of BC,CA,ABBC,CA,AB; DEFDEF has a quarter of the area.
Area of a triangle
13× asked, last 2025
Δ=12∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣\Delta=\tfrac12\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|
Zero: collinear. ∣E∣=2Δ|E|=2\Delta gives two parallel lines for the third vertex. Common vertex: area ratio = base ratio.
Rotation of a point
5× asked, last 2026
(x,y)→(xcos⁡θ−ysin⁡θ, xsin⁡θ+ycos⁡θ)(x,y)\to(x\cos\theta-y\sin\theta,\ x\sin\theta+y\cos\theta)
Anticlockwise about O. Images: in y=xy=x: (y,x)(y,x); xx-axis: (x,−y)(x,-y); origin: (−x,−y)(-x,-y).

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Practise Straight Lines

20 more formulas in 5 topics

Centres of a triangle; Slope, angle and forms of a line; Intersection, concurrency and position; Distances, foot and image; and Angle bisectors, family of lines, locus. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Centres of a triangle

  • Centroid10×
  • Incentre and inradius3×
  • Circumcentre7×
  • Orthocentre9×
  • Euler line6×

Slope, angle and forms of a line

  • Slope and angle11×
  • Slope, point, two-point forms6×
  • Intercept form7×
  • Normal form4×
  • Parametric form4×

Intersection, concurrency and position

  • Intersection8×
  • Concurrency3×
  • Side of a line6×

Distances, foot and image

  • Point to line17×
  • Parallel lines5×
  • Foot and image11×
  • Reflected ray7×

Angle bisectors, family of lines, locus

  • Angle bisectors10×
  • Family through a point4×
  • Locus13×

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About 130 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Straight Lines

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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