Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 127 · 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.In which quadrant does the point (6, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (7, 10) and (9, 0)? (a) (5, 8) (b) (8, 5) (c) (16, 10) (d) (1, 5)
3. 3.What is the distance between the points (9, 13) and (33, 6)? (a) 25 (b) 625 (c) 31 (d) 26
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
5. 5.What is the midpoint of the line joining (8, 10) and (18, 14)? (a) (12, 13) (b) (5, 2) (c) (26, 24) (d) (13, 12)
6. 6.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
8. 8.What is the midpoint of the line joining (0, 6) and (6, 2)? (a) (3, 4) (b) (4, 3) (c) (3, 2) (d) (6, 8)
9. 9.What is the distance between the points (2, 15) and (8, 7)? (a) 11 (b) 100 (c) 14 (d) 10
10. 10.In which quadrant does the point (−6, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
12. 12.In which quadrant does the point (−6, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
13. 13.What is the midpoint of the line joining (10, 3) and (14, 9)? (a) (6, 12) (b) (12, 6) (c) (24, 12) (d) (2, 3)
14. 14.What is the midpoint of the line joining (7, 1) and (19, 5)? (a) (26, 6) (b) (6, 2) (c) (3, 13) (d) (13, 3)
15. 15.What is the distance between the points (0, 8) and (15, 0)? (a) 18 (b) 23 (c) 289 (d) 17
16. 16.What is the midpoint of the line joining (5, 4) and (13, 2)? (a) (4, 1) (b) (18, 6) (c) (3, 9) (d) (9, 3)
17. 17.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
19. 19.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
20. 20.What is the distance between the points (5, 6) and (17, 22)? (a) 400 (b) 28 (c) 21 (d) 20
21. 21.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
22. 22.What is the midpoint of the line joining (10, 7) and (18, 11)? (a) (9, 14) (b) (4, 2) (c) (28, 18) (d) (14, 9)
23. 23.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
24. 24.What is the distance between the points (6, 6) and (13, 30)? (a) 625 (b) 25 (c) 26 (d) 31
25. 25.What is the distance between the points (0, 7) and (16, 19)? (a) 21 (b) 400 (c) 28 (d) 20
26. 26.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
27. 27.What is the distance between the points (0, 0) and (6, 8)? (a) 14 (b) 100 (c) 10 (d) 11
28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
29. 29.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
30. 30.What is the distance between the points (2, 2) and (14, 18)? (a) 21 (b) 28 (c) 20 (d) 400
31. 31.In which quadrant does the point (−9, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
32. 32.What is the distance between the points (1, 0) and (4, 4)? (a) 25 (b) 6 (c) 5 (d) 7
33. 33.In which quadrant does the point (4, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
34. 34.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
35. 35.What is the distance between the points (9, 4) and (21, 20)? (a) 20 (b) 21 (c) 28 (d) 400
36. 36.In which quadrant does the point (−4, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
37. 37.What is the distance between the points (8, 14) and (13, 2)? (a) 14 (b) 17 (c) 169 (d) 13
38. 38.In which quadrant does the point (9, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
39. 39.In which quadrant does the point (−8, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
40. 40.What is the midpoint of the line joining (2, 17) and (8, 9)? (a) (13, 5) (b) (3, 4) (c) (5, 13) (d) (10, 26)

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