Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 996 · 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 distance between the points (1, 15) and (17, 3)? (a) 400 (b) 28 (c) 21 (d) 20
2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
3. 3.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
4. 4.What is the distance between the points (3, 7) and (6, 3)? (a) 25 (b) 7 (c) 6 (d) 5
5. 5.What is the distance between the points (3, 29) and (10, 5)? (a) 31 (b) 26 (c) 625 (d) 25
6. 6.What is the distance between the points (8, 12) and (13, 0)? (a) 169 (b) 17 (c) 14 (d) 13
7. 7.What is the distance between the points (0, 15) and (24, 8)? (a) 31 (b) 625 (c) 25 (d) 26
8. 8.In which quadrant does the point (−2, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.In which quadrant does the point (−7, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
10. 10.What is the distance between the points (0, 2) and (3, 6)? (a) 5 (b) 7 (c) 25 (d) 6
11. 11.What is the midpoint of the line joining (4, 17) and (10, 7)? (a) (7, 12) (b) (14, 24) (c) (3, 5) (d) (12, 7)
12. 12.In which quadrant does the point (9, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
13. 13.What is the midpoint of the line joining (5, 2) and (13, 12)? (a) (9, 7) (b) (7, 9) (c) (18, 14) (d) (4, 5)
14. 14.What is the distance between the points (9, 14) and (18, 2)? (a) 21 (b) 225 (c) 16 (d) 15
15. 15.What is the distance between the points (9, 11) and (21, 6)? (a) 14 (b) 169 (c) 17 (d) 13
16. 16.What is the midpoint of the line joining (9, 1) and (19, 5)? (a) (5, 2) (b) (14, 3) (c) (3, 14) (d) (28, 6)
17. 17.What is the midpoint of the line joining (3, 3) and (11, 1)? (a) (2, 7) (b) (4, 1) (c) (7, 2) (d) (14, 4)
18. 18.What is the midpoint of the line joining (6, 8) and (16, 16)? (a) (12, 11) (b) (5, 4) (c) (22, 24) (d) (11, 12)
19. 19.What is the distance between the points (5, 5) and (20, 13)? (a) 18 (b) 17 (c) 289 (d) 23
20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
21. 21.What is the distance between the points (3, 5) and (10, 29)? (a) 25 (b) 31 (c) 26 (d) 625
22. 22.In which quadrant does the point (−7, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
23. 23.What is the distance between the points (4, 7) and (9, 19)? (a) 17 (b) 169 (c) 13 (d) 14
24. 24.What is the distance between the points (0, 7) and (3, 3)? (a) 6 (b) 25 (c) 5 (d) 7
25. 25.What is the midpoint of the line joining (2, 9) and (10, 17)? (a) (6, 13) (b) (13, 6) (c) (4, 4) (d) (12, 26)
26. 26.What is the midpoint of the line joining (0, 0) and (4, 6)? (a) (4, 6) (b) (3, 3) (c) (3, 2) (d) (2, 3)
27. 27.What is the midpoint of the line joining (2, 5) and (10, 17)? (a) (12, 22) (b) (11, 6) (c) (4, 6) (d) (6, 11)
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 (3, 18) and (8, 6)? (a) 17 (b) 169 (c) 14 (d) 13
30. 30.What is the distance between the points (6, 6) and (14, 21)? (a) 289 (b) 23 (c) 17 (d) 18
31. 31.What is the midpoint of the line joining (0, 7) and (4, 9)? (a) (4, 16) (b) (2, 1) (c) (8, 2) (d) (2, 8)
32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
34. 34.What is the midpoint of the line joining (6, 4) and (16, 16)? (a) (11, 10) (b) (10, 11) (c) (5, 6) (d) (22, 20)
35. 35.What is the midpoint of the line joining (2, 5) and (6, 11)? (a) (2, 3) (b) (8, 4) (c) (8, 16) (d) (4, 8)
36. 36.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
37. 37.What is the distance between the points (8, 2) and (20, 11)? (a) 16 (b) 21 (c) 225 (d) 15
38. 38.What is the midpoint of the line joining (3, 3) and (5, 7)? (a) (8, 10) (b) (4, 5) (c) (5, 4) (d) (1, 2)
39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14

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