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Saturday, 31 October

JEE Main · Maths · Three Dimensional Geometry

Image of a Point in a Line

JEE Main asked Image of a Point in a Line 16 times in 16 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2024, 2025 and 2026. It belongs to Lines in 3D, in Three Dimensional Geometry (Maths). The longest wait between two years asking it was 2 years. In 2022, 2024 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
16
in 16 shifts
Years
6 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.30.60’170.08’200.03’210.07’220’230.33’240.13’250.44’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 7 in 18 shifts · 2025: 1 in 8 shifts · 2026: 4 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20264 of 9
  • 20251 of 8
  • 20247 of 18
  • 20230 of 12
  • 20222 of 24
  • 20211 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Image of point in a line
  • Image of point in a line in 3d

Difficulty

Easy 0Medium 13Hard 3

5 of the 16 questions had a numerical answer.

Every question

All 16 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 6 Apr 2026, Shift 2 · Q24Let the image of the point P(0,−5,0)(0,-5,0) in the line x−12=y1=z+1−2\frac{x-1}{2}=\frac{y}{1}=\frac{z+1}{-2} be the point R and the image of the point…HardNumerical value
  2. 6 Apr 2026, Shift 1 · Q15Let the image of the point P(1,6,a)\mathrm{P}(1,6,a) in the line L:x1=y−12=z−a+1b\mathrm{L}:\frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}, b>0b>0, be…HardSingle correct
  3. 5 Apr 2026, Shift 2 · Q15If the distance of the point (a,2,5)(a, 2, 5) from the image of the point (1,2,7)(1, 2, 7) in the line x1=y−11=z−22\frac{x}{1}=\frac{y-1}{1}=\frac{z-2}{2} is…MediumSingle correct
  4. 4 Apr 2026, Shift 2 · Q14If (2α+1, α2−3α, α−12)\left(2\alpha+1,\,\alpha^2-3\alpha,\,\frac{\alpha-1}{2}\right) is the image of (α,2α,1)(\alpha,2\alpha,1) in the line…MediumSingle correct
  5. 2 Apr 2025, Shift 2 · Q14If the image of the point P(1,0,3)P(1, 0, 3) in the line joining the points A(4,7,1)A(4, 7, 1) and B(3,5,3)B(3, 5, 3) is Q(α,β,γ)Q(\alpha, \beta, \gamma), then…MediumSingle correct
  6. 31 Jan 2024, Shift 2 · Q16Let (α,β,γ)(\alpha,\beta,\gamma) be the mirror image of the point (2,3,5)(2,3,5) in the line x−12=y−23=z−34\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}. Then,…MediumSingle correct
  7. 1 Feb 2024, Shift 2 · Q15If the mirror image of the point P(3,4,9)P(3,4,9) in the line x−13=y+12=z−21\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1} is (α,β,γ)(\alpha,\beta,\gamma), then…MediumSingle correct
  8. 9 Apr 2024, Shift 2 · Q29The square of the distance of the image of the point (6,1,5)(6, 1, 5) in the line x−13=y2=z−24\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}, from the origin is…MediumNumerical value
  9. 8 Apr 2024, Shift 2 · Q29Let P(α,β,γ)P(\alpha, \beta, \gamma) be the image of the point Q(1,6,4)Q(1, 6, 4) in the line x1=y−12=z−23\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}. Then…MediumNumerical value
  10. 6 Apr 2024, Shift 2 · Q17Let P(α,β,γ)P(\alpha,\beta,\gamma) be the image of the point Q(3,−3,1)Q(3,-3,1) in the line x−01=y−31=z−1−1\frac{x-0}{1}=\frac{y-3}{1}=\frac{z-1}{-1} and RR be the…HardSingle correct
  11. 5 Apr 2024, Shift 2 · Q17Let (α,β,γ)(\alpha, \beta, \gamma) be the image of the point (8,5,7)(8, 5, 7) in the line x−12=y+13=z−25\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-2}{5}. Then…MediumSingle correct
  12. 4 Apr 2024, Shift 2 · Q29Consider a line L passing through the points P(1,2,1)P(1,2,1) and Q(2,1,−1)Q(2,1,-1). If the mirror image of the point A(2,2,2)A(2,2,2) in the line L is…MediumNumerical value
  13. 28 Jun 2022, Shift 2 · Q21Let the image of the point P(1, 2, 3) in the line L : x−63=y−12=z−23\frac{x-6}{3}=\frac{y-1}{2}=\frac{z-2}{3} be Q. Let R (α,β,γ)(\alpha, \beta, \gamma) be…MediumNumerical value
  14. 27 Jul 2022, Shift 2 · Q14If the length of the perpendicular drawn from the point P(a, 4, 2), a > 0 on the line x+12=y−33=z−1−1\frac{x+1}{2} = \frac{y-3}{3} = \frac{z-1}{-1} is…MediumSingle correct
  15. 24 Feb 2021, Shift 2 · Q61Let a, b ∈\in R. If the mirror image of the point P(a, 6, 9) with respect to the line x−37=y−25=z−1−9\frac{x-3}{7}=\frac{y-2}{5}=\frac{z-1}{-9} is…MediumSingle correct
  16. 5 Sep 2020, Shift 1 · Q66If (a, b, c) is the image of the point (1, 2, −3-3) in the line, x+12=y−3−2=z−1\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}, then a + b + c is equal to :MediumSingle correct

Shifts: 5 Sep 2020, Shift 1, 24 Feb 2021, Shift 2, 28 Jun 2022, Shift 2, 27 Jul 2022, Shift 2, 31 Jan 2024, Shift 2, 1 Feb 2024, Shift 2, 4 Apr 2024, Shift 2, 5 Apr 2024, Shift 2, 6 Apr 2024, Shift 2, 8 Apr 2024, Shift 2, 9 Apr 2024, Shift 2, 2 Apr 2025, Shift 2, 4 Apr 2026, Shift 2, 5 Apr 2026, Shift 2, 6 Apr 2026, Shift 2, 6 Apr 2026, Shift 1.

Same topic

Other ideas in Lines in 3D

Lines in 3D has 18 ideas JEE Main has asked; 10 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas