Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 882 · 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.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
2. 2.What is the midpoint of the line joining (7, 9) and (11, 13)? (a) (2, 2) (b) (9, 11) (c) (11, 9) (d) (18, 22)
3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
4. 4.What is the distance between the points (1, 5) and (6, 17)? (a) 14 (b) 17 (c) 169 (d) 13
5. 5.What is the midpoint of the line joining (0, 9) and (2, 7)? (a) (2, 16) (b) (8, 1) (c) (1, 1) (d) (1, 8)
6. 6.In which quadrant does the point (−1, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
9. 9.In which quadrant does the point (1, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
10. 10.What is the midpoint of the line joining (4, 9) and (10, 13)? (a) (14, 22) (b) (11, 7) (c) (3, 2) (d) (7, 11)
11. 11.What is the distance between the points (9, 7) and (25, 19)? (a) 20 (b) 21 (c) 400 (d) 28
12. 12.What is the distance between the points (5, 6) and (12, 30)? (a) 31 (b) 625 (c) 25 (d) 26
13. 13.What is the distance between the points (0, 4) and (16, 16)? (a) 20 (b) 400 (c) 21 (d) 28
14. 14.What is the distance between the points (6, 9) and (10, 12)? (a) 7 (b) 25 (c) 6 (d) 5
15. 15.In which quadrant does the point (−6, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
16. 16.In which quadrant does the point (−8, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
17. 17.What is the midpoint of the line joining (5, 9) and (9, 21)? (a) (7, 15) (b) (14, 30) (c) (15, 7) (d) (2, 6)
18. 18.In which quadrant does the point (−9, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
19. 19.What is the distance between the points (3, 26) and (10, 2)? (a) 625 (b) 31 (c) 26 (d) 25
20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
21. 21.What is the midpoint of the line joining (2, 4) and (4, 10)? (a) (1, 3) (b) (6, 14) (c) (3, 7) (d) (7, 3)
22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
23. 23.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
24. 24.What is the distance between the points (1, 1) and (17, 13)? (a) 400 (b) 20 (c) 21 (d) 28
25. 25.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
26. 26.What is the midpoint of the line joining (6, 8) and (10, 4)? (a) (2, 2) (b) (16, 12) (c) (8, 6) (d) (6, 8)
27. 27.What is the midpoint of the line joining (1, 7) and (11, 15)? (a) (12, 22) (b) (11, 6) (c) (6, 11) (d) (5, 4)
28. 28.What is the midpoint of the line joining (3, 6) and (15, 8)? (a) (6, 1) (b) (7, 9) (c) (18, 14) (d) (9, 7)
29. 29.What is the distance between the points (6, 31) and (13, 7)? (a) 26 (b) 625 (c) 25 (d) 31
30. 30.In which quadrant does the point (7, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
31. 31.In which quadrant does the point (−6, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
32. 32.What is the distance between the points (7, 10) and (19, 5)? (a) 13 (b) 14 (c) 169 (d) 17
33. 33.What is the distance between the points (2, 11) and (10, 5)? (a) 14 (b) 10 (c) 100 (d) 11
34. 34.What is the midpoint of the line joining (10, 7) and (22, 3)? (a) (32, 10) (b) (5, 16) (c) (16, 5) (d) (6, 2)
35. 35.What is the distance between the points (6, 2) and (9, 6)? (a) 7 (b) 25 (c) 5 (d) 6
36. 36.What is the midpoint of the line joining (9, 4) and (13, 14)? (a) (2, 5) (b) (11, 9) (c) (9, 11) (d) (22, 18)
37. 37.What is the midpoint of the line joining (4, 1) and (16, 3)? (a) (6, 1) (b) (10, 2) (c) (20, 4) (d) (2, 10)
38. 38.What is the midpoint of the line joining (6, 10) and (10, 8)? (a) (9, 8) (b) (2, 1) (c) (8, 9) (d) (16, 18)
39. 39.In which quadrant does the point (6, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
40. 40.What is the midpoint of the line joining (0, 8) and (4, 10)? (a) (2, 9) (b) (9, 2) (c) (4, 18) (d) (2, 1)

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