Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 651 · 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 (9, 2) and (12, 6)? (a) 6 (b) 5 (c) 25 (d) 7
2. 2.In which quadrant does the point (3, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
5. 5.What is the distance between the points (4, 8) and (16, 17)? (a) 21 (b) 16 (c) 225 (d) 15
6. 6.What is the midpoint of the line joining (10, 4) and (14, 6)? (a) (12, 5) (b) (2, 1) (c) (5, 12) (d) (24, 10)
7. 7.What is the distance between the points (3, 3) and (9, 11)? (a) 100 (b) 10 (c) 14 (d) 11
8. 8.What is the midpoint of the line joining (3, 14) and (13, 4)? (a) (16, 18) (b) (8, 9) (c) (5, 5) (d) (9, 8)
9. 9.What is the midpoint of the line joining (10, 11) and (14, 3)? (a) (24, 14) (b) (12, 7) (c) (2, 4) (d) (7, 12)
10. 10.What is the distance between the points (4, 15) and (12, 0)? (a) 289 (b) 18 (c) 17 (d) 23
11. 11.What is the midpoint of the line joining (9, 6) and (15, 0)? (a) (3, 12) (b) (3, 3) (c) (24, 6) (d) (12, 3)
12. 12.What is the midpoint of the line joining (0, 7) and (4, 15)? (a) (2, 4) (b) (2, 11) (c) (11, 2) (d) (4, 22)
13. 13.What is the midpoint of the line joining (2, 2) and (14, 12)? (a) (6, 5) (b) (7, 8) (c) (16, 14) (d) (8, 7)
14. 14.In which quadrant does the point (4, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
15. 15.What is the distance between the points (2, 0) and (26, 7)? (a) 31 (b) 25 (c) 26 (d) 625
16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
17. 17.In which quadrant does the point (4, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
18. 18.What is the distance between the points (6, 26) and (13, 2)? (a) 26 (b) 625 (c) 25 (d) 31
19. 19.What is the midpoint of the line joining (1, 9) and (11, 15)? (a) (12, 6) (b) (6, 12) (c) (12, 24) (d) (5, 3)
20. 20.What is the midpoint of the line joining (7, 5) and (19, 11)? (a) (8, 13) (b) (6, 3) (c) (26, 16) (d) (13, 8)
21. 21.In which quadrant does the point (−8, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
23. 23.What is the distance between the points (1, 8) and (13, 13)? (a) 13 (b) 169 (c) 17 (d) 14
24. 24.In which quadrant does the point (−4, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
25. 25.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
26. 26.What is the distance between the points (2, 5) and (11, 17)? (a) 16 (b) 225 (c) 15 (d) 21
27. 27.What is the midpoint of the line joining (4, 6) and (16, 8)? (a) (20, 14) (b) (6, 1) (c) (10, 7) (d) (7, 10)
28. 28.What is the distance between the points (4, 0) and (11, 24)? (a) 26 (b) 31 (c) 625 (d) 25
29. 29.In which quadrant does the point (3, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
30. 30.What is the distance between the points (0, 7) and (3, 3)? (a) 6 (b) 25 (c) 7 (d) 5
31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
32. 32.What is the distance between the points (9, 6) and (13, 9)? (a) 5 (b) 25 (c) 6 (d) 7
33. 33.What is the distance between the points (0, 7) and (5, 19)? (a) 13 (b) 169 (c) 17 (d) 14
34. 34.What is the midpoint of the line joining (2, 4) and (8, 0)? (a) (2, 5) (b) (5, 2) (c) (10, 4) (d) (3, 2)
35. 35.What is the distance between the points (2, 2) and (7, 14)? (a) 14 (b) 13 (c) 169 (d) 17
36. 36.What is the midpoint of the line joining (7, 9) and (17, 11)? (a) (10, 12) (b) (5, 1) (c) (12, 10) (d) (24, 20)
37. 37.What is the midpoint of the line joining (3, 1) and (7, 7)? (a) (10, 8) (b) (2, 3) (c) (5, 4) (d) (4, 5)
38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
39. 39.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
40. 40.What is the distance between the points (9, 2) and (16, 26)? (a) 25 (b) 31 (c) 625 (d) 26

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