Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 588 · 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, 8) and (13, 32)? (a) 26 (b) 625 (c) 25 (d) 31
2. 2.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
3. 3.What is the distance between the points (8, 2) and (15, 26)? (a) 625 (b) 31 (c) 26 (d) 25
4. 4.What is the distance between the points (3, 8) and (19, 20)? (a) 20 (b) 400 (c) 21 (d) 28
5. 5.In which quadrant does the point (2, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
6. 6.What is the midpoint of the line joining (8, 10) and (18, 0)? (a) (5, 13) (b) (5, 5) (c) (13, 5) (d) (26, 10)
7. 7.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
8. 8.In which quadrant does the point (6, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
9. 9.What is the distance between the points (7, 17) and (19, 1)? (a) 21 (b) 400 (c) 28 (d) 20
10. 10.What is the midpoint of the line joining (4, 6) and (16, 16)? (a) (20, 22) (b) (11, 10) (c) (6, 5) (d) (10, 11)
11. 11.What is the distance between the points (7, 6) and (11, 9)? (a) 7 (b) 25 (c) 6 (d) 5
12. 12.What is the distance between the points (9, 3) and (33, 10)? (a) 25 (b) 26 (c) 625 (d) 31
13. 13.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
14. 14.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
16. 16.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
17. 17.In which quadrant does the point (7, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
18. 18.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
19. 19.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
20. 20.What is the distance between the points (6, 7) and (30, 0)? (a) 25 (b) 625 (c) 26 (d) 31
21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
22. 22.What is the distance between the points (4, 24) and (12, 9)? (a) 289 (b) 17 (c) 23 (d) 18
23. 23.What is the distance between the points (8, 4) and (16, 19)? (a) 18 (b) 23 (c) 17 (d) 289
24. 24.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
25. 25.What is the midpoint of the line joining (9, 8) and (15, 14)? (a) (24, 22) (b) (12, 11) (c) (11, 12) (d) (3, 3)
26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
27. 27.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the distance between the points (2, 8) and (14, 17)? (a) 21 (b) 225 (c) 16 (d) 15
29. 29.What is the distance between the points (2, 23) and (10, 8)? (a) 18 (b) 289 (c) 23 (d) 17
30. 30.What is the distance between the points (8, 0) and (13, 12)? (a) 169 (b) 14 (c) 13 (d) 17
31. 31.What is the distance between the points (4, 7) and (16, 16)? (a) 21 (b) 16 (c) 225 (d) 15
32. 32.In which quadrant does the point (9, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
33. 33.In which quadrant does the point (−2, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
34. 34.What is the midpoint of the line joining (1, 7) and (5, 3)? (a) (3, 5) (b) (2, 2) (c) (6, 10) (d) (5, 3)
35. 35.In which quadrant does the point (6, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (1, 13) and (11, 1)? (a) (7, 6) (b) (5, 6) (c) (12, 14) (d) (6, 7)
37. 37.What is the distance between the points (2, 4) and (6, 1)? (a) 6 (b) 25 (c) 5 (d) 7
38. 38.What is the midpoint of the line joining (7, 8) and (9, 20)? (a) (16, 28) (b) (8, 14) (c) (14, 8) (d) (1, 6)
39. 39.In which quadrant does the point (9, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
40. 40.What is the midpoint of the line joining (1, 6) and (3, 18)? (a) (4, 24) (b) (1, 6) (c) (2, 12) (d) (12, 2)

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