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NCERT Class 10 Mathematics – Chapter 7: Coordinate Geometry
Board Exam 2026 focused online test strictly based on NCERT textbook.
- Coordinates are written as (x, y).
- Distance formula is derived using Pythagoras theorem.
- Mid-point formula finds the middle of a line segment.
- Section formula divides a line segment internally.
- Coordinate geometry is also called analytical geometry.
Q1. Distance between (0,0) and (3,4) is:
5
7
1
√7
√(3²+4²)=5.
Q2. Distance formula is based on:
Similarity
Pythagoras theorem
Area theorem
Mid-point theorem
NCERT derivation.
Q3. Mid-point of (2,4) and (6,8) is:
(2,6)
(8,12)
(4,6)
(3,5)
((2+6)/2,(4+8)/2).
Q4. Coordinates are written as:
(y,x)
[x,y]
{x,y}
(x,y)
Standard form.
Q5. If x=0, the point lies on:
Y-axis
X-axis
Origin
Quadrant I
x=0 on Y-axis.
Q6. Distance between (1,2) and (4,6) is:
4
5
6
7
√((3)²+(4)²)=5.
Q7. Mid-point of (0,0) and (2,2) is:
(1,2)
(2,1)
(1,1)
(0,1)
((0+2)/2,(0+2)/2).
Q8. Section formula divides a line:
Externally only
Vertically
Horizontally
Internally
NCERT scope.
Q9. Origin coordinates are:
(0,0)
(1,0)
(0,1)
(1,1)
Definition.
Q10. Distance formula between (x1,y1) and (x2,y2) is:
√((x2-x1)+(y2-y1))
√((x2-x1)²+(y2-y1)²)
(x2-x1)+(y2-y1)
(x2+y2)
NCERT formula.
Q11. Mid-point formula is:
(x1+x2,y1+y2)
(x1/2,y1/2)
((x1+x2)/2,(y1+y2)/2)
(x2/2,y2/2)
NCERT formula.
Q12. Coordinate geometry is also called:
Plane geometry
Solid geometry
Synthetic geometry
Analytical geometry
NCERT term.
Q13. Distance between identical points is:
0
1
2
Undefined
Same point.
Q14. Point (3,0) lies on:
Y-axis
X-axis
Origin
Quadrant I
y=0.
Q15. Distance between (−1,−1) and (2,3) is:
4
3
5
6
√(3²+4²)=5.
Q16. Mid-point of (−2,2) and (2,−2) is:
(1,1)
(−1,−1)
(0,1)
(0,0)
Average.
Q17. If y=0, the point lies on:
X-axis
Y-axis
Origin
Quadrant II
y=0.
Q18. Distance between (1,1) and (1,4) is:
2
3
4
5
Vertical distance.
Q19. Mid-point of endpoints of diameter of circle is:
Any point
On circle
Centre
Vertex
NCERT idea.
Q20. Coordinates lie in how many dimensions?
1
3
4
2
Plane.
Q21. Distance formula uses squares of:
Differences
Sums
Products
Ratios
Squared differences.
Q22. Section formula in this chapter is for:
External division
Internal division
Both
None
NCERT scope.
Q23. Distance between (0,5) and (0,−5) is:
5
8
10
0
Vertical distance.
Q24. Coordinates of mid-point of x-axis segment is:
(x,0)
(0,y)
(x,y)
(x/2,0)
y=0.
Q25. Distance between (−3,4) and (0,0) is:
5
7
3
4
√(9+16)=5.
Q26. Mid-point of (1,−1) and (3,3) is:
(2,1)
(2,1)
(1,2)
(3,1)
Average.
Q27. Coordinates are ordered pairs because:
Any order
Random
Order matters
Size matters
x then y.
Q28. Point (0,0) is called:
Axis
Intercept
Vertex
Origin
Definition.
Q29. Distance between (2,3) and (2,7) is:
4
5
6
7
Vertical distance.
Q30. Mid-point lies:
Outside segment
On segment
Outside plane
At origin
Definition.
Q31. Distance formula gives:
Slope
Area
Length
Angle
Length.
Q32. Coordinates of a point determine its:
Color
Shape
Size
Position
Position.
Q33. Distance between (−1,0) and (1,0) is:
2
1
0
3
Horizontal distance.
Q34. Mid-point of (0,2) and (4,2) is:
(2,0)
(2,2)
(0,2)
(4,2)
Average.
Q35. Distance formula contains:
Cube
Product
Square root
Division
Square root.
Q36. Coordinate geometry studies:
Solids
Angles
Areas
Points using coordinates
NCERT scope.
Q37. Distance between (5,5) and (5,5) is:
0
5
10
Undefined
Same point.
Q38. Mid-point formula uses:
Difference
Average
Product
Ratio
Average.
Q39. Distance between (0,−3) and (4,0) is:
3
4
5
6
√(16+9)=5.
Q40. Coordinates represent:
Area
Length
Angle
Location
Location.
Q41. Distance between (−4,0) and (0,3) is:
5
7
1
3
√(16+9)=5.
Q42. Mid-point of (−2,4) and (2,4) is:
(0,2)
(0,4)
(2,0)
(4,0)
Average.
Q43. Distance formula measures:
Angle
Slope
Straight line distance
Area
Length.
Q44. Coordinate geometry helps in:
Only drawing
Only measurement
Only algebra
Algebraic study of geometry
NCERT concept.
Q45. Distance between (6,8) and (0,0) is:
10
12
14
8
√(36+64)=10.
Q46. Mid-point lies exactly:
Near one end
Halfway between points
Outside segment
At origin
Definition.
Q47. Coordinates of a point are:
Three numbers
Single number
Ordered pair
Unordered pair
(x,y).
Q48. Distance formula applies to:
Only horizontal
Only vertical
Only diagonal
Any two points
General formula.
Q49. Mid-point of (a,b) and (c,d) is:
((a+c)/2,(b+d)/2)
(a+c,b+d)
(a/2,b/2)
(c/2,d/2)
Formula.
Q50. Main objective of this chapter is:
Trigonometry
Study of points using coordinates
Mensuration
Statistics
NCERT objective.
📘 NCERT Class 10 Maths – Chapter-wise Online Tests
- Chapter 1: Real Numbers – Online Test
- Chapter 2: Polynomials – Online Test
- Chapter 3: Pair of Linear Equations in Two Variables – Online Test
- Chapter 4: Quadratic Equations – Online Test
- Chapter 5: Arithmetic Progressions – Online Test
- Chapter 6: Triangles – Online Test
- Chapter 7: Coordinate Geometry – Online Test
- Chapter 8: Introduction to Trigonometry – Online Test
- Chapter 9: Applications of Trigonometry – Online Test
- Chapter 10: Circles – Online Test
- Chapter 11: Areas Related to Circles – Online Test
- Chapter 12: Surface Areas and Volumes – Online Test
- Chapter 13: Statistics – Online Test
- Chapter 14: Probability – Online Test
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