CBSE Class 10 Mathematics (Standard) Chapter 7 Coordinate Geometry Important Questions 2027
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25 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 3.6 questions per paper (OR alternatives counted separately)
- 5 question patterns repeated across papers
Important topics in Coordinate Geometry
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Distance formula | Board 2023Board 2024Board 2025Sample 2025Sample 2026 | ★★★☆☆ |
| 2 | Section formula (internal division) | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Points on axes / collinearity via distance-section | Board 2023Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 4 | Midpoint formula | Board 2024Board 2025Board 2026Sample 2026 | ★★☆☆☆ |
Repeated questions from Coordinate Geometry
1. Point dividing segment in a given ratio
2×Sample 2025Sample 20261/2 marks
[case context: Class X students on picnic; positions of friends shown as points P(2,5), Q(4,4), R(8,3)] Let S be a point which divides the line joining PQ in ratio 2:3. Find the coordinates of S.
2. Perpendicular distance of a point from an axis
2×Board 2026Sample 20261 marks
The distance of the point A(4a, 3a) from x-axis is : (A) 3a (B) -3a (C) 4a (D) -4a
3. Find ratio of division (by axis or given point)
3×Board 2023Board 2024Board 20251/3 marks
Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the point of intersection.
4. Distance between two given points
2×Board 2023Sample 20261 marks
[case context: Class X students on picnic; positions of friends Aman, Kirti, Chahat shown as points P(2,5), Q(4,4), R(8,3) on a coordinate grid] Find the distance between P and R.
5. Unknown coordinate from given distance
2×Board 2024Sample 20251/2 marks
Find the point(s) on the x-axis which is at a distance of sqrt(41) units from the point (8, -5).
Coordinate Geometry questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 4 | 6 |
| Board 2024 | 5 | 9 |
| Board 2025 | 3 | 6 |
| Sample 2025 | 4 | 6 |
| Board 2026 | 3 | 6 |
| Sample 2026 | 6 | 8 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Coordinate Geometry
Board 2026 3 questions
The distance of the point A(4a, 3a) from x-axis is : (A) 3a (B) -3a (C) 4a (D) -4a
If the points A(4, 5), B(m, 6), C(4, 3) and D(1, n) taken in this order are the vertices of a parallelogram ABCD, then find the values of m and n.
Find the coordinates of the points of trisection of the line segment joining the points A(-1, 4) and B(-3, -2).
Sample 2026 6 questions
The shortest distance (in units) of the point (2,3) from y-axis is (A) 2 (B) 3 (C) 5 (D) 1
The points A(9,0), B(9,-6), C(-9,0) and D(-9,6) are the vertices of a (A) Square (B) Rectangle (C) Parallelogram (D) Trapezium
[case context: Class X students on picnic; positions of friends Aman, Kirti, Chahat shown as points P(2,5), Q(4,4), R(8,3) on a coordinate grid] Find the distance between P and R.
[case context: Class X students on picnic; positions of friends shown as points P(2,5), Q(4,4), R(8,3)] Is Q the midpoint of PR? Justify by finding midpoint of PR.
[case context: Class X students on picnic; positions of friends shown as points P(2,5), Q(4,4), R(8,3)] Find the point on x-axis which is equidistant from P and Q.
[case context: Class X students on picnic; positions of friends shown as points P(2,5), Q(4,4), R(8,3)] Let S be a point which divides the line joining PQ in ratio 2:3. Find the coordinates of S.
Board 2025 3 questions
The mid-point of the line segment joining the points P(-4, 5) and Q(4, 6) lies on : (A) x-axis (B) y-axis (C) origin (D) neither x-axis nor y-axis
The coordinates of the centre of a circle are (2a, a - 7). Find the value(s) of 'a' if the circle passes through the point (11, -9) and has diameter 10*sqrt(2) units.
Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also find the point of intersection.
Sample 2025 4 questions
The point on the x-axis nearest to the point (-4,-5) is A) (0,0) B) (-4,0) C) (-5,0) D) (sqrt(41),0)
A point on the x-axis divides the line segment joining the points A(2,-3) and B(5,6) in the ratio 1:2. The point is A) (4,0) B) (7/2, 3/2) C) (3,0) D) (0,3)
Find the point(s) on the x-axis which is at a distance of sqrt(41) units from the point (8, -5).
Show that the points A(-5,6), B(3,0) and C(9,8) are the vertices of an isosceles triangle.
Board 2024 5 questions
AD is a median of triangle ABC with vertices A(5, -6), B(6, 4) and C(0, 0). Length AD is equal to: (a) sqrt(68) units (b) 2*sqrt(15) units (c) sqrt(101) units (d) 10 units
If the distance between the points (3, -5) and (x, -5) is 15 units, then the values of x are: (a) 12, -18 (b) -12, 18 (c) 18, 5 (d) -9, -12
The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at: (a) (0, 0) (b) (4, 0) (c) (-2, 0) (d) (-6, 0)
Find the ratio in which the point (8/5, y) divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.
ABCD is a rectangle formed by the points A(-1, -1), B(-1, 6), C(3, 6) and D(3, -1). P, Q, R and S are mid-points of sides AB, BC, CD and DA respectively. Show that diagonals of the quadrilateral PQRS bisect each other.
Board 2023 4 questions
In what ratio, does x-axis divide the line segment joining the points A(3, 6) and B(-12, -3)? (A) 1 : 2 (B) 1 : 4 (C) 4 : 1 (D) 2 : 1
The distance between the points (0, 2 sqrt(5)) and (-2 sqrt(5), 0) is (A) 2 sqrt(10) units (B) 4 sqrt(10) units (C) 2 sqrt(20) units (D) 0
Assertion (A): Point P(0, 2) is the point of intersection of y-axis with the line 3x + 2y = 4. Reason (R): The distance of point P(0, 2) from x-axis is 2 units. Select: (A) Both A and R true, R correct explanation (B) Both true, R not correct explanation (C) A true, R false (D) A false, R true
If (-5, 3) and (5, 3) are two vertices of an equilateral triangle, then find co-ordinates of the third vertex, given that origin lies inside the triangle. (Take sqrt(3) = 1.7)
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 7 Coordinate Geometry?
By how often and how recently they were asked: Distance formula; Section formula (internal division); Points on axes / collinearity via distance-section.
How many marks does Coordinate Geometry carry in the CBSE Class 10 Mathematics (Standard) 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 3.6 questions per paper.
Do questions from Coordinate Geometry repeat in board exams?
Yes — 5 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.