Coordinate Geometry Questions for SSC CGL: Quick Overview
Below are 20 original coordinate geometry questions written in the SSC CGL and CHSL pattern, each solved in one or two lines, plus the trap that catches most candidates on that type. In the SSC syllabus, this area appears as "Graphs of Linear Equations" under Algebra, alongside triangle and circle geometry (SSC CGL 2026 notice, para 13.11.1.3–13.11.1.4). In practice it means: distance, section formula, area of a triangle, straight lines, reflections and the triangle made by a line with the axes.
Key takeaway: most SSC coordinate questions are one formula plus one substitution. The marks are lost on signs (negative coordinates), on unequal coefficients in the parallel-lines distance, and on forgetting the second value in "find x" questions.
The formulas themselves are on our Coordinate Geometry Formulas for SSC CGL page; this page uses different numbers and more question types, so do both.
Set A: Distance and Section Formula (Q1–Q6)
Q1. Find the distance between (−1, 3) and (5, −5). (a) 8 (b) 10 (c) 12 (d) 14 Answer: (b) 10. √(6² + 8²) = 10.
Q2. The distance between (x, 2) and (3, −2) is 5 units. Find x. (a) 6 only (b) 0 only (c) 0 or 6 (d) 3 or −3 Answer: (c). (x − 3)² + 16 = 25 gives x − 3 = ±3. Trap: most candidates stop at x = 6.
Q3. In what ratio does the x-axis divide the line joining (2, −3) and (5, 6)? (a) 1 : 2 (b) 2 : 1 (c) 1 : 3 (d) 3 : 1 Answer: (a) 1 : 2. On the x-axis y = 0: ratio = −y₁ : y₂ = 3 : 6.
Q4. Find the point that divides the join of (−3, 5) and (7, −5) internally in the ratio 3 : 2. (a) (3, −1) (b) (2, 1) (c) (1, 3) (d) (3, 1) Answer: (a). x = (3 × 7 + 2 × (−3))/5 = 3; y = (3 × (−5) + 2 × 5)/5 = −1.
Q5. A(1, 2), B(4, 3) and C(6, 6) are three vertices of parallelogram ABCD. Find D. (a) (3, 5) (b) (9, 7) (c) (−1, −1) (d) (4, 6) Answer: (a). Diagonals bisect each other: D = A + C − B = (1 + 6 − 4, 2 + 6 − 3).
Q6. The centroid of a triangle is (2, 3) and two vertices are (1, 1) and (4, 2). Find the third vertex. (a) (1, 6) (b) (2, 6) (c) (1, 5) (d) (3, 4) Answer: (a). Third vertex = (3 × 2 − 5, 3 × 3 − 3).
Set B: Area and Collinearity (Q7–Q10)
Q7. Find the area of the triangle with vertices (0, 0), (6, 0) and (2, 5). (a) 12 (b) 15 (c) 18 (d) 30 Answer: (b) 15 sq units. Base 6 on the x-axis, height 5: ½ × 6 × 5.
Q8. Find the area of the quadrilateral with vertices (0, 0), (4, 0), (5, 3) and (1, 4), taken in order. (a) 12 (b) 14 (c) 14.5 (d) 29 Answer: (c) 14.5 sq units. Shoelace: ½ |0 + 12 + 17 + 0| = 29/2. Trap: forgetting the ½ gives 29.
Q9. Find k if (k, 1), (2, 3) and (4, 7) are collinear. (a) 0 (b) 1 (c) 2 (d) −1 Answer: (b) 1. Slope of the last two points is 2, so (3 − 1)/(2 − k) = 2.
Q10. Find the area of the triangle formed by the line 3x + 4y = 24 and the coordinate axes. (a) 12 (b) 24 (c) 48 (d) 96 Answer: (b) 24 sq units. Intercepts are 8 and 6; area = ½ × 8 × 6. Shortcut: for ax + by = c, area = c²/(2|ab|) = 576/24.
Set C: Straight Lines (Q11–Q16)
Q11. Find the equation of the line through (2, −1) parallel to 4x − 3y + 1 = 0. (a) 4x − 3y − 11 = 0 (b) 3x + 4y − 2 = 0 (c) 4x − 3y + 11 = 0 (d) 4x + 3y − 5 = 0 Answer: (a). Parallel lines keep the same x and y coefficients: 4(2) − 3(−1) = 11.
Q12. Find the line through (1, 2) perpendicular to x + 2y = 5. (a) 2x − y = 0 (b) x − 2y + 3 = 0 (c) 2x + y = 4 (d) x + 2y = 5 Answer: (a). Swap the coefficients and change one sign: 2x − y = 2(1) − 2 = 0.
Q13. Where do x + y = 7 and 2x − y = 2 intersect? (a) (2, 5) (b) (3, 4) (c) (4, 3) (d) (5, 2) Answer: (b). Adding gives 3x = 9.
Q14. Find k if 2x + ky = 3 and 4x + 6y = 7 are parallel. (a) 2 (b) 3 (c) 4 (d) 12 Answer: (b) 3. 2/4 = k/6.
Q15. A line passes through (0, 3) and makes an angle of 135° with the positive x-axis. Find its equation. (a) x − y + 3 = 0 (b) x + y = 3 (c) y = x + 3 (d) x + y + 3 = 0 Answer: (b). Slope = tan 135° = −1, so y = −x + 3.
Q16. Find the distance of (2, −1) from the line 5x + 12y − 11 = 0. (a) 1 (b) 13 (c) 23/13 (d) 2 Answer: (a) 1. |10 − 12 − 11|/√(25 + 144) = 13/13.
Set D: Parallel Lines, Reflections and Centres (Q17–Q20)
Q17. Find the distance between the parallel lines 6x + 8y − 15 = 0 and 3x + 4y + 5 = 0. (a) 1 (b) 2 (c) 2.5 (d) 4 Answer: (c) 2.5. First make the coefficients equal: 6x + 8y + 10 = 0. Then |−15 − 10|/10. Trap: using the formula directly gives a wrong answer.
Q18. Find the image of (4, −7) in the line y = x. (a) (−4, 7) (b) (−7, 4) (c) (7, −4) (d) (4, 7) Answer: (b). Reflection in y = x swaps the coordinates.
Q19. Find the circumcentre of the triangle with vertices (0, 0), (8, 0) and (0, 6). (a) (4, 3) (b) (8/3, 2) (c) (2, 2) (d) (3, 4) Answer: (a). It is a right triangle (right angle at the origin), so the circumcentre is the midpoint of the hypotenuse. Circumradius = 5.
Q20. Find the incentre of the triangle with vertices A(0, 0), B(6, 0) and C(0, 8). (a) (2, 2) (b) (3, 4) (c) (2, 8/3) (d) (1, 1) Answer: (a). Sides opposite A, B, C are 10, 8, 6. Incentre = ((10 × 0 + 8 × 6 + 6 × 0)/24, (10 × 0 + 8 × 0 + 6 × 8)/24) = (2, 2). Check: inradius of a 6-8-10 triangle is (6 + 8 − 10)/2 = 2.
Answer Key
| Q | Ans | Q | Ans | Q | Ans | Q | Ans |
|---|---|---|---|---|---|---|---|
| 1 | b | 6 | a | 11 | a | 16 | a |
| 2 | c | 7 | b | 12 | a | 17 | c |
| 3 | a | 8 | c | 13 | b | 18 | b |
| 4 | a | 9 | b | 14 | b | 19 | a |
| 5 | a | 10 | b | 15 | b | 20 | a |
The 6 Traps in SSC Coordinate Geometry
| Trap | How to avoid it |
|---|---|
| Only one root in "find x" distance questions | Always write ± after the square root |
| Sign errors with negative coordinates | Put negative numbers in brackets before squaring |
| Missing ½ in area | Write "½ × (absolute value)" before you start |
| Unequal coefficients in parallel-line distance | Make the x and y coefficients identical first |
| Internal vs external division | External uses a minus sign in the numerator and denominator |
| Reflection in y = −x | (a, b) becomes (−b, −a), not (b, a) |
Practise Under Time
- Full sectional test: SSC CGL Tier 1 mock: Geometry and Coordinate Geometry
- SSC CGL coordinate geometry mock test 01, 02, 03
- Triangle and circle practice: Geometry questions for SSC CGL (25 solved)
Coordinate Geometry Questions FAQs
Is coordinate geometry in the SSC CGL syllabus?
Yes. The SSC CGL 2026 notice lists "Graphs of Linear Equations" under Algebra in both Tier 1 and Tier 2, and questions on distance, section formula, area and straight lines are asked under it.
What is the fastest way to find the area of a triangle made by a line with the axes?
For ax + by = c, the area is c²/(2|ab|). For 3x + 4y = 24 that is 576/24 = 24 square units.
How do I find the distance between two parallel lines?
Make the x and y coefficients the same, then use |c₁ − c₂| / √(a² + b²).
How do I check whether three points are collinear?
Either check that the slopes between pairs are equal, or check that the area of the triangle they form is zero.
Is coordinate geometry asked in SSC CHSL Tier 1?
The SSC CHSL 2026 notice lists "Graphs of Linear Equations" in its Quantitative Aptitude syllabus too, and CHSL Tier 1 runs from 30 November to 31 December 2026 (SSC notice, 01.10.2026).
Practice Next for SSC CGL Maths
- Formulas: Coordinate geometry formulas for SSC CGL, Algebra formulas for SSC CGL, Geometry formulas
- Plan: SSC CGL Tier 2 preparation strategy 2026
- Mocks: SSC CGL algebra mock test 01, SSC CGL geometry mock test 02
Sources: SSC CGL 2026 notice (syllabus para 13.11.1); SSC CHSL 2026 notice; SSC notice dated 01.10.2026. Questions and solutions are original BookOfExams material. Last checked 7 November 2026.