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Step-by-step NCERT solutions for Coordinate Geometry (Chapter 7, CBSE Class 10 Mathematics) — the full working for every question, not just the final answer. You can also read the Coordinate Geometry textbook chapter.

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All 20 questions in Coordinate Geometry are solved in the PDF. Here's what's inside, exercise by exercise:

Distance Formula

  1. Find the distance between the following pairs of points:
    • (i) (2, 3) and (4, 1)
    • (ii) (−5, 7) and (−1, 3)
    • (iii) (a, b) and (−a, −b)
  2. Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2?
  3. Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
  4. Check whether (5, −2), (6, 4) and (7, −2) are the vertices of an isosceles triangle.
  5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, "Don't you think ABCD is a square?" Chameli disagrees. Using distance formula, find which of them is correct. [From Fig. 7.8: A(3, 4), B(6, 7), C(9, 4), D(6, 1)]
  6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
    • (i) (−1, −2), (1, 0), (−1, 2), (−3, 0)
    • (ii) (−3, 5), (3, 1), (0, 3), (−1, −4)
    • (iii) (4, 5), (7, 6), (4, 3), (1, 2)
  7. Find the point on the x-axis which is equidistant from (2, −5) and (−2, 9).
  8. Find the values of y for which the distance between the points P(2, −3) and Q(10, y) is 10 units.
  9. If Q(0, 1) is equidistant from P(5, −3) and R(x, 6), find the values of x. Also find the distances QR and PR.
  10. Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).

Section Formula

  1. Find the coordinates of the point which divides the join of (−1, 7) and (4, −3) in the ratio 2 : 3.
  2. Find the coordinates of the points of trisection of the line segment joining (4, −1) and (−2, −3).
  3. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag. What is the…
  4. Find the ratio in which the line segment joining the points (−3, 10) and (6, −8) is divided by (−1, 6).
  5. Find the ratio in which the line segment joining A(1, −5) and B(−4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
  6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.
  7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, −3) and B is (1, 4).
  8. If A and B are (−2, −2) and (2, −4), respectively, find the coordinates of P such that AP = (3/7)AB and P lies on the line segment AB.
  9. Find the coordinates of the points which divide the line segment joining A(−2, 2) and B(2, 8) into four equal parts.
  10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (−1, 4) and (−2, −1) taken in order. [Hint: Area of a rhombus = (1/2) × (product of its diagonals)]
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More NCERT Solutions for Class 10

Read the Coordinate Geometry textbook chapter / PDF, or browse all CBSE Class 10 Mathematics solutions.

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