Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 155 · 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 (6, 2) and (15, 14)? (a) 225 (b) 15 (c) 16 (d) 21
2. 2.What is the distance between the points (9, 14) and (14, 2)? (a) 13 (b) 169 (c) 17 (d) 14
3. 3.What is the midpoint of the line joining (8, 13) and (18, 9)? (a) (5, 2) (b) (26, 22) (c) (13, 11) (d) (11, 13)
4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
5. 5.In which quadrant does the point (−5, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
6. 6.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
7. 7.What is the distance between the points (5, 4) and (9, 7)? (a) 7 (b) 25 (c) 5 (d) 6
8. 8.What is the midpoint of the line joining (3, 16) and (5, 8)? (a) (1, 4) (b) (4, 12) (c) (12, 4) (d) (8, 24)
9. 9.What is the midpoint of the line joining (7, 0) and (11, 10)? (a) (5, 9) (b) (2, 5) (c) (18, 10) (d) (9, 5)
10. 10.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
11. 11.What is the distance between the points (8, 11) and (11, 7)? (a) 25 (b) 7 (c) 6 (d) 5
12. 12.What is the distance between the points (2, 6) and (9, 30)? (a) 26 (b) 31 (c) 625 (d) 25
13. 13.What is the midpoint of the line joining (6, 3) and (12, 5)? (a) (3, 1) (b) (9, 4) (c) (18, 8) (d) (4, 9)
14. 14.What is the midpoint of the line joining (7, 4) and (9, 2)? (a) (16, 6) (b) (8, 3) (c) (1, 1) (d) (3, 8)
15. 15.In which quadrant does the point (4, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
17. 17.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
19. 19.What is the distance between the points (1, 0) and (7, 8)? (a) 100 (b) 11 (c) 14 (d) 10
20. 20.What is the midpoint of the line joining (2, 6) and (8, 4)? (a) (5, 5) (b) (3, 1) (c) (10, 10) (d) (6, 5)
21. 21.What is the distance between the points (4, 16) and (28, 9)? (a) 31 (b) 625 (c) 26 (d) 25
22. 22.What is the distance between the points (2, 7) and (5, 3)? (a) 5 (b) 6 (c) 7 (d) 25
23. 23.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
26. 26.What is the midpoint of the line joining (2, 7) and (6, 1)? (a) (4, 4) (b) (2, 3) (c) (8, 8) (d) (5, 4)
27. 27.What is the midpoint of the line joining (2, 6) and (4, 0)? (a) (1, 3) (b) (4, 3) (c) (3, 3) (d) (6, 6)
28. 28.What is the distance between the points (6, 13) and (18, 8)? (a) 13 (b) 14 (c) 169 (d) 17
29. 29.What is the midpoint of the line joining (7, 16) and (9, 10)? (a) (8, 13) (b) (13, 8) (c) (16, 26) (d) (1, 3)
30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
31. 31.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
32. 32.What is the midpoint of the line joining (2, 10) and (14, 20)? (a) (6, 5) (b) (16, 30) (c) (15, 8) (d) (8, 15)
33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
34. 34.What is the midpoint of the line joining (5, 6) and (11, 4)? (a) (5, 8) (b) (16, 10) (c) (8, 5) (d) (3, 1)
35. 35.What is the distance between the points (8, 8) and (15, 32)? (a) 625 (b) 31 (c) 26 (d) 25
36. 36.What is the midpoint of the line joining (2, 10) and (10, 6)? (a) (12, 16) (b) (4, 2) (c) (6, 8) (d) (8, 6)
37. 37.What is the midpoint of the line joining (1, 0) and (5, 2)? (a) (2, 1) (b) (1, 3) (c) (6, 2) (d) (3, 1)
38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
39. 39.What is the midpoint of the line joining (1, 0) and (11, 10)? (a) (5, 6) (b) (12, 10) (c) (5, 5) (d) (6, 5)
40. 40.In which quadrant does the point (5, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant

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