THE GOAL • CBSE CLASS 10

COORDINATE GEOMETRY

Chapter 7 • Basic Mathematics • 2025 PYQs

CBSE 2025 Basic Mathematics Previous Year Questions Chapter-wise Collection

Chapter 7: Coordinate Geometry

Unique Previous Year Questions from the CBSE Class 10 Basic Mathematics 2025 paper sets, covering coordinate concepts, distance formula, section formula, midpoint, collinearity and case-study applications.

I

Multiple Choice Questions

1. Basic Concepts
1 Mark
For a point \((3,-5)\), the value of \[ \text{abscissa}-\text{ordinate} \] is:
(A) \(-8\)
(B) \(-2\)
(C) \(2\)
(D) \(8\)
Set 430/1/1
2. Mid-point Ratio
1 Mark
The mid-point of a line segment divides the line segment in the ratio:
(A) \(1:2\)
(B) \(2:1\)
(C) \(1:1\)
(D) \(\frac12:2\)
Set 430/1/1
3. Coordinate Distance
1 Mark
The distance of a point \(P(3,-7)\) from the \(y\)-axis is:
(A) \(3\)
(B) \(7\)
(C) \(-7\)
(D) \(\sqrt{58}\)
Set 430/1/2
4. Literal Coordinates
1 Mark
For a point \(X(a,b)\), where \(b>a>0\), the value of \[ [\text{distance from }x\text{-axis}] - [\text{distance from }y\text{-axis}] \] is:
(A) \(a-b\)
(B) \(b-a\)
(C) \(a^2-b^2\)
(D) \(b^2-a^2\)
Set 430/1/3
5. Distance from Origin
1 Mark
The distance of the point \((2,3)\) from the origin is:
(A) \(2\)
(B) \(3\)
(C) \(5\)
(D) \(\sqrt{13}\)
Set 430/2/1
6. Mid-point and Axis
1 Mark
The mid-point of the line segment joining the points \((1,3)\) and \((1,-3)\) lies:
(A) at the origin
(B) in the second quadrant
(C) on \(x\)-axis
(D) on \(y\)-axis
Set 430/2/1
7. Mid-point with Variables
1 Mark
If point \((1,2)\) is the mid-point of the line segment joining the points \((3,5)\) and \((2a,b)\), then \((a,b)=\):
(A) \((-1,-1)\)
(B) \(\left(-\frac12,-\frac12\right)\)
(C) \(\left(-\frac12,-1\right)\)
(D) \(\left(-1,-\frac12\right)\)
Set 430/3/1
8. Alternative Mid-point
1 Mark
If point \((a,2b)\) is the mid-point of the line segment joining the points \((3,5)\) and \((-1,-1)\), then \((a,b)\) is equal to:
(A) \((1,2)\)
(B) \((2,2)\)
(C) \((2,1)\)
(D) \((1,1)\)
Set 430/3/3
9. Distance Calculation
1 Mark
The distance between the points \((2,3)\) and \((-2,-3)\) is:
(A) \(4\sqrt{13}\)
(B) \(\sqrt{40}\)
(C) \(2\sqrt{13}\)
(D) \(5\)
Set 430/5/1
10. Section Ratio
1 Mark
The point \((x,0)\) divides the line segment joining the points \((-4,5)\) and \((0,-10)\) in the ratio:
(A) \(1:3\)
(B) \(2:1\)
(C) \(1:1\)
(D) \(1:2\)
Set 430/5/1
11. Distance – Alternative
1 Mark
The distance between the points \((2,-7)\) and \((-2,-1)\) is:
(A) \(10\)
(B) \(2\sqrt{13}\)
(C) \(8\)
(D) \(4\sqrt{13}\)
Set 430/4/2
12. Geometric Figure Data
1 Mark
ABCD is a rectangle with its vertices at \[ (2,-2),\;(8,4),\;(4,8),\;(-2,2) \] taken in order. The length of its diagonal is:
(A) \(4\sqrt2\)
(B) \(6\sqrt2\)
(C) \(4\sqrt{26}\)
(D) \(2\sqrt{26}\)
Set 430/6/1
13. Line Equation and Point
1 Mark
The point \((3,-5)\) lies on the line \[ mx-y=11. \] The value of \(m\) is:
(A) \(3\)
(B) \(-2\)
(C) \(8\)
(D) \(2\)
Set 430/6/3
II

Very Short Answer Type Questions

14. Section Formula
2 Marks
The line segment joining \((2,8)\) and \((-3,-5)\) is divided by point \(P(x,0)\) in a fixed ratio. Find that ratio and the value of \(x\).
Set 430/4/1
15. Trisection of a Line Segment
2 Marks
Find the coordinates of the points of trisection of the line segment joining the points \[ (-4,1)\quad\text{and}\quad(6,5). \]
Set 430/5/1
16. Collinearity
2 Marks
Using distance formula, prove that the points \[ (1,5),\quad(2,3),\quad(3,1) \] are collinear.
Set 430/5/1
17. Equidistant Relation
2 Marks
Establish a relation between \(x\) and \(y\) such that the point \((x,y)\) is equidistant from the points \[ (-2,5)\quad\text{and}\quad(3,9). \]
Set 430/5/2
III

Short Answer Type Questions

18. Parallelogram Property
3 Marks
If the points \[ A(-5,y),\quad B(2,-2),\quad C(8,4),\quad D(x,5) \] are the vertices of a parallelogram \(ABCD\), taken in order, find the values of \(x\) and \(y\). Hence, find the lengths of the sides of this parallelogram.
Set 430/4/2
IV

Case Study Based Questions

19. Figure-Based – Circular Park
4 Marks

In a society, there is a circular park having two gates placed at \[ A(10,20)\quad\text{and}\quad B(50,50). \] Two fountains are installed at \(P\) and \(Q\) on \(AB\) such that \[ AP=PQ=QB. \]

(i) Find the coordinates of the centre \(C\). 1 Mark
(ii) Find the radius of the circular park. 1 Mark
(iii) Find the coordinates of point \(P\). 2 Marks
OR Find the distance of the fountain at \(Q\) from gate \(A\). 2 Marks
Set 430/1/1
20. Figure-Based – Rectangular Field
4 Marks

A rectangular field \(ABCD\) has vertices \[ A(10,10),\quad B(40,10),\quad C(40,50),\quad D(x,y). \] Anita moves from \(A\) to \(E\), the point of intersection of the diagonals. Anil runs from \(C\) to \(A\) via \(D\).

(i) Find the coordinates of point \(E\). 1 Mark
(ii) Find the distance between points \(B\) and \(C\). 1 Mark
(iii) Find the coordinates of point \(D\) and distance \(BD\). 2 Marks
OR Find the total distance travelled by Anita. 2 Marks
Set 430/2/1
21. Figure-Based – Semicircular Park
4 Marks

A semicircular park has a diameter \(AB\), where \[ A(2,3)\quad\text{and}\quad B(22,3). \] A borewell is situated at the centre \(O\).

(i) Find the coordinates of point \(O\). 1 Mark
(ii) Find the radius of the semicircular park. 1 Mark
(iii) A sapling is at \(C(12,y)\) on the boundary. Find \(C\). 2 Marks
OR A sapling is at \(P\) on \(AB\) such that \[ PA=\frac13PB. \] Find the coordinates of \(P\). 2 Marks
Set 430/3/1
22. Graph-Based – Robot Path
4 Marks

A robot moves from \((0,0)\) to \(P(8,6)\), then to \(Q(12,2)\), and ends at \(S(-6,6)\) in straight lines.

(i) Determine the distance \(OP\). 1 Mark
(ii) Line \(QS\) is \[ 2x+9y=42. \] Find the coordinates of the point where it intersects the \(y\)-axis. 1 Mark
(iii) Point \(R(4.8,y)\) divides segment \(OP\) in a certain ratio. Find the ratio and \(y\). 2 Marks
OR Using distance formula, show that \[ \frac{PQ}{OS}=\frac23. \] 2 Marks
Set 430/6/1