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Class 10 Maths Chapter 7: Coordinate Geometry — Important Questions & Sample Paper

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Reviewed by qpaper's CBSE curriculum team · Edited by Mohit · Updated June 2026

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Yes — this page has 44+ original Class 10 Mathematics Chapter 7 (“Coordinate Geometry”) important questions with answers (Multiple Choice (MCQ), Assertion–Reason, Short Answer, Short Answer, Long Answer, Case Study). Practise them free, or generate a full CBSE board-pattern sample paper (80 marks) and export it to PDF or Word — in English & Hindi, for 2026-27.

Coordinate Geometry in Class 10 bridges algebra and geometry, allowing you to study geometric shapes on the Cartesian plane using coordinates. This chapter focuses on three fundamental concepts: the distance formula, the section formula, and the area of a triangle. You learn to calculate the distance between two points using Pythagoras' theorem, find the coordinates of a point that divides a line segment internally in a given ratio, and compute the area of a triangle when its vertices are known. The midpoint formula is a special case of the section formula. Additionally, you explore the centroid of a triangle and how to test if three points are collinear. In exams, you'll encounter a variety of problems—from straightforward distance and midpoint calculations to more involved questions like determining the ratio in which a point divides a segment, finding unknown coordinates using given distances or areas, and applying the section formula to points that are 'twice as far' from one endpoint. Mastering these skills not only secures marks in Chapter 7 but also builds a strong foundation for higher-level coordinate geometry. With qpaper.in, you can generate unlimited CBSE-style practice papers tailored to this chapter, helping you confidently tackle any question type.

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Mathematics — Coordinate Geometry

Class 10Time: 3 hrsMax Marks: 80

SECTION A

  1. 1.

    For what value of k are the points (7,-2), (5,1), and (3,k) collinear?

    (a) 4(b) 2(c) -4(d) -2
    1
  2. 2.

    The area of a triangle with vertices (1,0), (6,0), and (4,4) is:

    (a) 10 square units(b) 20 square units(c) 5 square units(d) 12 square units
    1
  3. 3.

    Which of the following points lies on the x-axis?

    (a) (0,4)(b) (4,0)(c) (4,4)(d) (0,0)
    1

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Marks distribution & blueprint

In a CBSE exam, this chapter typically contributes questions across the following types. The last column shows how many original questions of each type we have ready in our bank for this chapter:

Question typeMarks eachIn our bank
Multiple Choice (MCQ)1 mark13
Assertion–Reason1 mark6
Short Answer2 marks8
Short Answer3 marks6
Long Answer5 marks5
Case Study4 marks6

44 original, exam-style questions in our bank for this chapter — with answers.

Important & sample questions (with answers)

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  1. Q1. For what value of k are the points (7,-2), (5,1), and (3,k) collinear?

    1 mark
    Multiple Choice (MCQ)
    (A) 4(B) 2(C) -4(D) -2
    ▸ Answer

    4

  2. Q2. The area of a triangle with vertices (1,0), (6,0), and (4,4) is:

    1 mark
    Multiple Choice (MCQ)
    (A) 10 square units(B) 20 square units(C) 5 square units(D) 12 square units
    ▸ Answer

    10 square units

  3. Q3. Which of the following points lies on the x-axis?

    1 mark
    Multiple Choice (MCQ)
    (A) (0,4)(B) (4,0)(C) (4,4)(D) (0,0)
    ▸ Answer

    (4,0)

  4. Q4. If the distance between the points (3, a) and (6, 1) is 5 units, then the possible value(s) of a is/are:

    1 mark
    Multiple Choice (MCQ)
    (A) -3(B) 5(C) -3 or 5(D) 3 or -5
    ▸ Answer

    -3 or 5

  5. Q5. Assertion (A): The area of the triangle with vertices (0,0), (4,0) and (0,3) is 6 square units. Reason (R): The area is obtained by multiplying the x-intercept and y-intercept, giving 4×3=12.

    1 mark
    Assertion–Reason
    (A) Both A and R are true and R is the correct explanation of A.(B) Both A and R are true but R is not the correct explanation of A.(C) A is true but R is false.(D) A is false but R is true.
    ▸ Answer

    A is true but R is false.

  6. Q6. Find the distance between the points A(2, 3) and B(5, 7).

    2 marks
    Short Answer
    ▸ Answer

    5 units

  7. Q7. If the distance between the points (4, p) and (1, 0) is 5 units, find the value of p.

    2 marks
    Short Answer
    ▸ Answer

    p = 4 or p = -4

  8. Q8. Find the midpoint of the line segment joining the points A(-4, 6) and B(2, -8).

    3 marks
    Short Answer
    ▸ Answer

    (-1, -1)

  9. Q9. Find the distance between the points (2, -3) and (10, 6).

    3 marks
    Short Answer
    ▸ Answer

    √145 units

  10. Q10. Show that the points A(1, 5), B(2, 3) and C(4, –1) are collinear. Hence find the ratio AB : BC.

    5 marks
    Long Answer
    ▸ Answer

    The points are collinear and AB : BC = 1 : 2.

  11. Q11. Find the area of the quadrilateral whose vertices are A(–3, –1), B(–2, –4), C(4, –1) and D(3, 4).

    5 marks
    Long Answer
    ▸ Answer

    28 square units

  12. Q12. A land survey maps three corners of a plot as A(3, 4), B(7, 8), and C(5, 10). The surveyor needs to check if these points are collinear. If not, they plan to build a triangular garden and want to know its area.

    4 marks
    Case Study
    1. (i) Determine if points A, B, C are collinear.1 mark
    2. (ii) Find the area of the triangle formed by A, B, C.2 marks
    3. (iii) Find the length of the median from B to side AC.1 mark
    ▸ Answer

    Not collinear; Area = 8 sq. units; Median length = √10 units.

Frequently asked questions

What is the distance formula in coordinate geometry?

For two points A(x₁, y₁) and B(x₂, y₂), the distance AB = √[(x₂ - x₁)² + (y₂ - y₁)²]. This is derived from the Pythagorean theorem and is used to find the length of a line segment on the Cartesian plane.

How do you find the coordinates of a point dividing a line segment in a given ratio?

Use the section formula for internal division: if a point P divides the segment joining A(x₁, y₁) and B(x₂, y₂) in the ratio m:n, then P's coordinates are ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n)). The midpoint formula is a special case when m = n.

How is the area of a triangle calculated using coordinates?

Given vertices A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), the area = ½|x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|. The absolute value ensures the area is positive. This formula also helps check collinearity—if the area is zero, the points are collinear.

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