CBSE Class 10 Mathematics (Basic) Chapter 7 Coordinate Geometry Important Questions 2027
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31 questions from Coordinate Geometry appeared in 6 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Coordinate Geometry unit — 6 marks in the official syllabus
- Asked in 6 of 7 analysed papers (2022–2026)
- About 4.4 questions per paper (OR alternatives counted separately)
- 7 question patterns repeated across papers
Important topics in Coordinate Geometry
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Distance formula | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 2 | Midpoint formula | Board 2024Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
| 3 | Section formula (internal division) | Board 2023Board 2024Board 2025Board 2026Sample 2025 | ★☆☆☆☆ |
| 4 | Points on axes / collinearity via distance-section | Board 2025Board 2026Sample 2026 | ★☆☆☆☆ |
Repeated questions from Coordinate Geometry
1. Distance between two given points
5×Board 2023Board 2024Sample 2025Sample 20261 marks
The distance between the points (cos30°, sin30°) and (cos60°, −sin60°) is
A) 0 unit
B) √3 units
C) 1 unit
D) √2 units
2. Find the midpoint given endpoints
4×Board 2024Board 2025Board 2026Sample 20261 marks
[Case: A circular park has two gates at A(10, 20) and B(50, 50); two fountains at P and Q lie on AB such that AP = PQ = QB.] Find the coordinates of the centre C.
3. Point dividing a segment in a given ratio
3×Board 2023Board 2025Board 20262 marks
[Case: A circular park has two gates at A(10, 20) and B(50, 50); two fountains at P and Q lie on AB such that AP = PQ = QB.] Find the coordinates of the point P.
4. Evaluate an expression in abscissa and ordinate
2×Board 2025Board 20261 marks
For a point (3, – 5), the value of (abscissa – ordinate) is : (A) – 8 (B) – 2 (C) 2 (D) 8
5. Ratio in which the midpoint divides a segment
2×Board 2025Board 20261 marks
The mid-point of a line segment divides the line segment in the ratio : (A) 1 : 2 (B) 2 : 1 (C) 1 : 1 (D) 1/2 : 2
6. Radius = half the distance between diameter endpoints
2×Board 2025Board 20261 marks
[Case: A circular park has two gates at A(10, 20) and B(50, 50); two fountains at P and Q lie on AB such that AP = PQ = QB.] Find the radius of the circular park.
7. Distance of a section point from an endpoint
2×Board 2025Board 20262 marks
[Case: A circular park has two gates at A(10, 20) and B(50, 50); two fountains at P and Q lie on AB such that AP = PQ = QB.] Find the distance of the fountain at Q from gate A.
Coordinate Geometry questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 4 | 8 |
| Board 2024 | 4 | 6 |
| Board 2025 | 6 | 8 |
| Sample 2025 | 5 | 11 |
| Board 2026 | 6 | 8 |
| Sample 2026 | 6 | 8 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Coordinate Geometry
Board 2026 6 questions
For a point (3, – 5), the value of (abscissa – ordinate) is : (A) – 8 (B) – 2 (C) 2 (D) 8
The mid-point of a line segment divides the line segment in the ratio : (A) 1 : 2 (B) 2 : 1 (C) 1 : 1 (D) 1/2 : 2
[Case: A circular park has two gates at A(10, 20) and B(50, 50); two fountains at P and Q lie on AB such that AP = PQ = QB.] Find the coordinates of the centre C.
[Case: A circular park has two gates at A(10, 20) and B(50, 50); two fountains at P and Q lie on AB such that AP = PQ = QB.] Find the radius of the circular park.
[Case: A circular park has two gates at A(10, 20) and B(50, 50); two fountains at P and Q lie on AB such that AP = PQ = QB.] Find the coordinates of the point P.
[Case: A circular park has two gates at A(10, 20) and B(50, 50); two fountains at P and Q lie on AB such that AP = PQ = QB.] Find the distance of the fountain at Q from gate A.
Sample 2026 6 questions
The distance between the points (cos30°, sin30°) and (cos60°, −sin60°) is
A) 0 unit
B) √3 units
C) 1 unit
D) √2 units
The co-ordinates of the point which is mirror image of the point (−3, 5) about x-axis are
A) (3, 5)
B) (3, −5)
C) (−3, −5)
D) (−3, 5)
[Carpooling: three friends Amar, Bhavin and Chetanya live at A(4,5), B(6,2) and C(2,6); their common office is at O(0,0).] What is the distance between B and C?
[Carpooling: three friends Amar, Bhavin and Chetanya live at A(4,5), B(6,2) and C(2,6); their common office is at O(0,0).] If Bhavin and Chetanya planned to meet at a club situated at the mid-point of the line joining the points B and C, find the coordinates of this point.
[Carpooling: three friends Amar, Bhavin and Chetanya live at A(4,5), B(6,2) and C(2,6); their common office is at O(0,0).] Which society is farthest from the office? Also find its distance from the office.
[Carpooling: three friends Amar, Bhavin and Chetanya live at A(4,5), B(6,2) and C(2,6); their common office is at O(0,0).] Out of B and C which society is nearer to A? Also find their distances.
Board 2025 6 questions
For a point (3, -5), the value of (abscissa - ordinate) is : (A) -8 (B) -2 (C) 2 (D) 8
The mid-point of a line segment divides the line segment in the ratio : (A) 1 : 2 (B) 2 : 1 (C) 1 : 1 (D) 1/2 : 2
[Case context: A circular park has two gates at points A(10, 20) and B(50, 50); fountains P and Q lie on AB such that AP = PQ = QB.] Find the coordinates of the centre C.
[Case context: A circular park with gates A(10, 20) and B(50, 50) as diameter endpoints.] Find the radius of the circular park.
[Case context: Gates A(10, 20) and B(50, 50); fountains P and Q on AB with AP = PQ = QB.] Find the coordinates of the point P.
[Case context: Gates A(10, 20) and B(50, 50); fountains P and Q on AB with AP = PQ = QB.] Find the distance of the fountain at Q from gate A.
Sample 2025 5 questions
The distance between the points (a, b) and (−a, −b) is (A) √(a2 + b2) (B) a2 + b2 (C) 2√(a2 + b2) (D) 4√(a2 + b2)
P(x, y) is a point equidistant from the points A(4, 3) and B(3, 4). Prove that x − y = 0.
In the given figure, △ABC is an equilateral triangle. Coordinates of vertices A and B are (0, 3) and (0, −3) respectively. Find the coordinates of point C.
Find the ratio in which the y-axis divides the line segment joining the points (4, −5) and (−1, 2). Also find the point of intersection.
Line 4x + y = 4 divides the line segment joining the points (−2, −1) and (3, 5) in a certain ratio. Find the ratio.
Board 2024 4 questions
The mid-point of the line segment joining the points (-1, 3) and (8, 3/2) is : (a) (7/2, -3/4) (b) (7/2, 9/2) (c) (9/2, -3/4) (d) (7/2, 9/4)
The distance between the points (2, -3) and (-2, 3) is : (a) 2√13 units (b) 5 units (c) 13√2 units (d) 10 units
The diameter of a circle is of length 6 cm. If one end of the diameter is (-4, 0), the other end on x-axis is at : (a) (0, 2) (b) (6, 0) (c) (2, 0) (d) (4, 0)
Find the co-ordinates of the points of trisection of the line segment joining the points (-2, 2) and (7, -4).
Board 2023 4 questions
The distance between the points (3, 0) and (0, −3) is : (a) 2√3 units (b) 6 units (c) 3 units (d) 3√2 units
Find the coordinates of the point which divides the line segment joining the points (7, −1) and (−3, 4) internally in the ratio 2 : 3.
Find the value(s) of y for which the distance between the points A(3, −1) and B(11, y) is 10 units.
Show that the points A(1, 7), B(4, 2), C(−1, −1) and D(− 4, 4) are vertices of the square ABCD.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) Chapter 7 Coordinate Geometry?
By how often and how recently they were asked: Distance formula; Midpoint formula; Section formula (internal division).
How many marks does Coordinate Geometry carry in the CBSE Class 10 Mathematics (Basic) exam?
Coordinate Geometry is part of the Coordinate Geometry unit, which carries 6 marks in the official syllabus. In the analysed papers it had about 4.4 questions per paper.
Do questions from Coordinate Geometry repeat in board exams?
Yes — 7 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.