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Straight Lines

NCERT Class 11 Mathematics Chapter 9

Straight Lines for Class 11 Maths and JEE: slope, angle between lines, the forms of the equation of a line and the distance of a point from a line.

6 topics Updated 8 Nov 2026

For: Class 11 and JEE, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 9 “Straight Lines”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.5 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Coordinate geometry basics

    Proofs, external division, mid-point, triangle area, collinear points and solved examples.

    NCERT Section 9.1 20 min read 6 solved examples 13 practice questions

  2. Locus and its equation

    Locus of a point for JEE Main: the P(h, k) method, perpendicular bisectors, circles, angle bisectors and loci with a parameter, with solved examples.

    JEE only 14 min read 5 solved examples 10 practice questions

  3. Slope of a line

    Inclination, m = tan θ, slope from two points, parallel and perpendicular lines and the angle between two lines.

    NCERT Section 9.2 17 min read 6 solved examples 12 practice questions

  4. Forms of the equation of a line

    Point-slope, two-point, slope-intercept, intercept and general forms, a formula sheet and solved NCERT questions.

    NCERT Section 9.3 17 min read 6 solved examples 26 practice questions

  5. Distance of a point from a line

    The formula and its proof, parallel lines, the foot of the perpendicular and the image of a point.

    NCERT Section 9.4 16 min read 7 solved examples 10 practice questions

  6. Intersection of lines and centres of a triangle

    Intersection of two lines for JEE Main: the formula, concurrent lines, and the centroid, circumcentre and orthocentre of a triangle, with solved examples.

    JEE only 17 min read 6 solved examples 13 practice questions

Key formulas in this chapter

Coordinate geometry basics

  • PQ = (x − x) + (y − y)
  • internal m: n: ((mx + nx)/(m + n), (my + ny)/(m + n))
  • external m: n: ((mx − nx)/(m − n), (my − ny)/(m − n)), m, n > 0, m ≠ n
  • mid-point: ((x + x)/2, (y + y)/2)
  • area = ½|x(y − y) + x(y − y) + x(y − y)|
  • collinear ⇔ x(y − y) + x(y − y) + x(y − y) = 0
  • polygon: ½|(xy − xy) + … + (xy − xy)|

Locus

  • P(h, k) on the locus → condition in h, k → replace h, k by x, y
  • PA = PB ⇔ P on the perpendicular bisector of AB (A ≠ B)
  • PC = r: (x − a) + (y − b) = r, r ≥ 0
  • rod of length l sliding on the axes, mid-point: x + y = l/4

Slope of a line

  • m = tan θ, θ ≠ 90°
  • m = (y − y)/(x − x), x ≠ x
  • distinct non-vertical lines parallel: m = m
  • perpendicular: mm = −1
  • tan θ = |(m − m)/(1 + mm)|, 1 + mm ≠ 0
  • A, B, C collinear ⇔ slope of AB = slope of BC (AB vertical: equal x-coordinates)

Forms of the equation of a line

  • horizontal: y = a; vertical: x = b
  • y − y = m(x − x)
  • y − y = ((y − y)/(x − x))(x − x), x ≠ x
  • y = mx + c; y = m(x − d)
  • x/a + y/b = 1 (a, b ≠ 0)
  • Ax + By + C = 0: slope −A/B (B ≠ 0); intercepts −C/A (A ≠ 0), −C/B (B ≠ 0)
  • parallel through (x, y): A(x − x) + B(y − y) = 0
  • perpendicular through (x, y): B(x − x) − A(y − y) = 0

Distance of a point from a line

  • d = |Ax + By + C| / √(A + B)
  • origin: d = |C| / √(A + B)
  • parallel lines: d = |C − C| / √(A + B)
  • y = mx + c, y = mx + c: d = |c − c| / √(1 + m)
  • foot: (h − x)/A = (k − y)/B = −(Ax + By + C)/(A + B), A, B ≠ 0
  • image: (h − x)/A = (k − y)/B = −2(Ax + By + C)/(A + B), A, B ≠ 0

Intersection of lines and triangle centres

  • D = ab − ab ≠ 0: x = (bc − bc)/D, y = (ca − ca)/D
  • parallel or the same line: ab − ab = 0
  • concurrent (no two parallel): a(bc − bc) + b(ca − ca) + c(ab − ab) = 0
  • through the intersection of L = 0 and L = 0: L + λL = 0
  • G = ((x + x + x)/3, (y + y + y)/3)
  • circumcentre O: OA = OB = OC
  • orthocentre H: meet of the altitudes; H = 3G − 2O

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