Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 436 · 40 questions

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

1. 1.What is the midpoint of the line joining (10, 6) and (18, 18)? (a) (12, 14) (b) (4, 6) (c) (28, 24) (d) (14, 12)
2. 2.What is the midpoint of the line joining (3, 0) and (15, 12)? (a) (6, 9) (b) (18, 12) (c) (9, 6) (d) (6, 6)
3. 3.In which quadrant does the point (9, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
5. 5.In which quadrant does the point (9, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
6. 6.What is the midpoint of the line joining (3, 19) and (9, 9)? (a) (12, 28) (b) (6, 14) (c) (14, 6) (d) (3, 5)
7. 7.What is the distance between the points (6, 4) and (10, 7)? (a) 7 (b) 25 (c) 5 (d) 6
8. 8.In which quadrant does the point (7, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
9. 9.In which quadrant does the point (7, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
10. 10.What is the midpoint of the line joining (0, 11) and (4, 7)? (a) (9, 2) (b) (2, 9) (c) (4, 18) (d) (2, 2)
11. 11.What is the midpoint of the line joining (2, 22) and (8, 10)? (a) (10, 32) (b) (16, 5) (c) (3, 6) (d) (5, 16)
12. 12.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
13. 13.What is the distance between the points (7, 2) and (15, 17)? (a) 289 (b) 18 (c) 23 (d) 17
14. 14.What is the distance between the points (1, 33) and (8, 9)? (a) 31 (b) 26 (c) 25 (d) 625
15. 15.What is the distance between the points (2, 20) and (10, 5)? (a) 289 (b) 18 (c) 23 (d) 17
16. 16.In which quadrant does the point (5, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
17. 17.What is the midpoint of the line joining (7, 1) and (17, 3)? (a) (24, 4) (b) (5, 1) (c) (12, 2) (d) (2, 12)
18. 18.What is the midpoint of the line joining (10, 1) and (16, 3)? (a) (3, 1) (b) (26, 4) (c) (13, 2) (d) (2, 13)
19. 19.What is the distance between the points (5, 9) and (29, 16)? (a) 26 (b) 625 (c) 25 (d) 31
20. 20.In which quadrant does the point (3, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
21. 21.What is the distance between the points (6, 0) and (18, 9)? (a) 16 (b) 225 (c) 21 (d) 15
22. 22.What is the distance between the points (8, 9) and (23, 17)? (a) 23 (b) 289 (c) 18 (d) 17
23. 23.In which quadrant does the point (4, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
24. 24.What is the distance between the points (6, 8) and (11, 20)? (a) 17 (b) 13 (c) 169 (d) 14
25. 25.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
26. 26.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
27. 27.What is the distance between the points (9, 1) and (15, 9)? (a) 10 (b) 100 (c) 11 (d) 14
28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
29. 29.What is the distance between the points (9, 21) and (17, 6)? (a) 23 (b) 289 (c) 18 (d) 17
30. 30.In which quadrant does the point (8, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
31. 31.In which quadrant does the point (−1, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.In which quadrant does the point (−7, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
33. 33.What is the midpoint of the line joining (9, 10) and (13, 20)? (a) (22, 30) (b) (2, 5) (c) (15, 11) (d) (11, 15)
34. 34.What is the midpoint of the line joining (1, 14) and (7, 6)? (a) (8, 20) (b) (10, 4) (c) (3, 4) (d) (4, 10)
35. 35.In which quadrant does the point (−2, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
36. 36.What is the distance between the points (9, 29) and (16, 5)? (a) 25 (b) 625 (c) 26 (d) 31
37. 37.What is the distance between the points (1, 13) and (4, 9)? (a) 25 (b) 5 (c) 7 (d) 6
38. 38.In which quadrant does the point (−5, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
39. 39.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
40. 40.What is the midpoint of the line joining (8, 14) and (18, 10)? (a) (26, 24) (b) (12, 13) (c) (13, 12) (d) (5, 2)

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad