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CBSE Class 10 Maths Chapter 7 Coordinate Geometry Model Questions - 3 Marks - Part 1
Deepa Maths Academy • Global Examination Portal

CBSE Class 10 Maths Chapter 7 Coordinate Geometry Model Questions - 3 Marks - Part 1

Secure University-Grade Repository for Model Assessments, Board Examinations, and Step-by-Step Solutions.

Portal ID: DMA-EXAM-2026 • Security: Encrypted • Status: Active Examination

SECTION C — Short Answer Type Questions [3 Marks Each]

  • 3 Marks Q1. Prove that the points A(3,0), B(6,4), and C(−1,3) are the vertices of a right-angled isosceles triangle.
  • 3 Marks Q2. Show that the points A(−4,−1), B(−2,−4), C(4,0), and D(2,3) are the vertices of a rectangle.
  • 3 Marks Q3. Find the coordinates of the circumcenter of the triangle whose vertices are A(3,0), B(−1,−3), and C(−1,5).
  • 3 Marks Q4. Prove that the points A(1,7), B(4,2), C(−1,−1), and D(−4,4) are the vertices of a square, but not a rhombus. (Verify diagonal lengths)
  • 3 Marks Q5. Find a relation between x and y such that the point (x,y) is equidistant from the points (7,1) and (3,5)
  • 3 Marks Q6. Determine if the points P(1,5), Q(2,3), and R(−2,−11) form a triangle. If yes, name the type of triangle based on side lengths.
  • 3 Marks Q7. Find the point on the x-axis which is equidistant from (2,−5) and (−2,9). Hence, find its distance from both points.
  • 3 Marks Q8. Prove that the points (a,0), (0,b), and (1,1) form a right-angled triangle if a21​+b21​=1
  • 3 Marks Q9. Find the values of y for which the distance between the points P(2,−3) and Q(10,y) is 10 units.
  • 3 Marks Q10. Show that the points A(a,a), B(−a,−a), and C(−3 ​a,3​a) are the vertices of an equilateral triangle.
  • 3 Marks Q11. Find the center of a circle passing through the points (6,−6), (3,−7), and (3,3).
  • 3 Marks Q12. If P(x,y) is any point equidistant from A(a+b,b−a) and B(a−b,a+b), prove that bx=ay.
  • 3 Marks Q13. Find the coordinates of the points which divide the line segment joining A(−2,2) and B(2,8) into four equal parts.
  • 3 Marks Q14. Find the ratio in which the line segment joining the points (−3,10) and (6,−8) is divided by (−1,6). Also find the length of both segments.
  • 3 Marks Q15. If the points A(6,1), B(8,2), C(9,4), and D(p,3) are the vertices of a parallelogram taken in order, find the value of p using mid-point properties.
  • 3 Marks Q16. Find the ratio in which the x-axis divides the line segment joining the points (1,−5) and (−4,5). Also find the coordinates of the point of intersection.
  • 3 Marks Q17. If A(−2,−2) and B(2,−4) are given, find the coordinates of P such that AP=73​AB where P lies on the line segment AB.
  • 3 Marks Q18. Find the coordinates of the point P on the line segment joining A(1,2) and B(6,7) such that AP=52​AB.
  • 3 Marks Q19. Find the ratio in which the line 2x+y−4=0 divides the line segment joining the points A(2,−2) and B(3,7).
  • 3 Marks Q20. If A(−1,3), B(1,−1), and C(5,1) are the vertices of a triangle ABC, find the length of the median through vertex A.
  • 3 Marks Q21. Find the coordinates of the vertices of a triangle whose mid-points of sides are (3,2), (4,−1), and (1,2).
  • 3 Marks Q22. If the points (1,2), (4,y), (x,6), and (3,5) are the vertices of a parallelogram taken in order, find x and y.
  • 3 Marks Q23. 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.
  • 3 Marks Q24. Two opposite vertices of a square are (−1,2) and (3,2). Find the coordinates of the other two vertices.
  • 3 Marks Q25. Find the coordinates of a point A, where AB is a diameter of a circle whose center is (2,−3) and B is (1,4).

Academic Repository Disclaimer & எச்சரிக்கை அறிவிப்பு :

English: These model solutions are structured to global academic standards for self-assessment and practice purposes. Students are advised to verify with official textbooks for board examinations.

தமிழ்: இந்த மாதிரி கணிதத் தீர்வுகள் மாணவர்களின் சுய கற்றல் மற்றும் பயிற்சித் திறனுக்காக உலகளாவிய கல்வித் தரத்தில் உருவாக்கப்பட்டுள்ளன. தேர்வுகளுக்குத் தயாராகும் போது உங்கள் அதிகாரப்பூர்வ பாடப்புத்தகத்துடன் சரிபார்க்கவும்.

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