Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 344 · 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, 8) and (17, 23)? (a) 23 (b) 289 (c) 18 (d) 17
2. 2.What is the distance between the points (4, 3) and (8, 6)? (a) 7 (b) 6 (c) 5 (d) 25
3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
4. 4.In which quadrant does the point (8, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
5. 5.What is the distance between the points (2, 18) and (7, 6)? (a) 17 (b) 13 (c) 169 (d) 14
6. 6.What is the distance between the points (9, 8) and (21, 13)? (a) 13 (b) 17 (c) 169 (d) 14
7. 7.What is the distance between the points (8, 8) and (32, 1)? (a) 625 (b) 31 (c) 25 (d) 26
8. 8.What is the midpoint of the line joining (4, 5) and (6, 7)? (a) (10, 12) (b) (5, 6) (c) (1, 1) (d) (6, 5)
9. 9.What is the midpoint of the line joining (8, 10) and (12, 12)? (a) (10, 11) (b) (2, 1) (c) (20, 22) (d) (11, 10)
10. 10.What is the distance between the points (1, 9) and (17, 21)? (a) 21 (b) 28 (c) 400 (d) 20
11. 11.What is the distance between the points (2, 21) and (10, 6)? (a) 18 (b) 17 (c) 289 (d) 23
12. 12.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
13. 13.What is the distance between the points (3, 11) and (27, 4)? (a) 31 (b) 625 (c) 26 (d) 25
14. 14.In which quadrant does the point (1, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
15. 15.In which quadrant does the point (−9, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
16. 16.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
17. 17.What is the midpoint of the line joining (8, 12) and (10, 6)? (a) (1, 3) (b) (9, 9) (c) (10, 9) (d) (18, 18)
18. 18.What is the distance between the points (7, 5) and (14, 29)? (a) 31 (b) 26 (c) 25 (d) 625
19. 19.What is the distance between the points (1, 7) and (25, 14)? (a) 31 (b) 26 (c) 25 (d) 625
20. 20.What is the distance between the points (1, 9) and (8, 33)? (a) 26 (b) 625 (c) 31 (d) 25
21. 21.What is the midpoint of the line joining (7, 11) and (13, 5)? (a) (3, 3) (b) (20, 16) (c) (10, 8) (d) (8, 10)
22. 22.What is the midpoint of the line joining (2, 13) and (14, 5)? (a) (6, 4) (b) (9, 8) (c) (16, 18) (d) (8, 9)
23. 23.What is the distance between the points (7, 19) and (16, 7)? (a) 16 (b) 225 (c) 21 (d) 15
24. 24.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
25. 25.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
26. 26.What is the midpoint of the line joining (3, 8) and (9, 20)? (a) (14, 6) (b) (12, 28) (c) (6, 14) (d) (3, 6)
27. 27.What is the distance between the points (4, 6) and (8, 9)? (a) 7 (b) 6 (c) 25 (d) 5
28. 28.What is the midpoint of the line joining (2, 0) and (10, 2)? (a) (4, 1) (b) (1, 6) (c) (12, 2) (d) (6, 1)
29. 29.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
30. 30.What is the distance between the points (1, 15) and (6, 3)? (a) 14 (b) 169 (c) 13 (d) 17
31. 31.What is the midpoint of the line joining (7, 11) and (15, 3)? (a) (7, 11) (b) (22, 14) (c) (11, 7) (d) (4, 4)
32. 32.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
33. 33.What is the midpoint of the line joining (2, 0) and (10, 4)? (a) (4, 2) (b) (12, 4) (c) (2, 6) (d) (6, 2)
34. 34.In which quadrant does the point (−6, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the midpoint of the line joining (10, 1) and (20, 11)? (a) (30, 12) (b) (15, 6) (c) (5, 5) (d) (6, 15)
36. 36.In which quadrant does the point (7, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
37. 37.What is the distance between the points (0, 7) and (8, 22)? (a) 17 (b) 23 (c) 289 (d) 18
38. 38.What is the distance between the points (4, 31) and (11, 7)? (a) 625 (b) 26 (c) 25 (d) 31
39. 39.In which quadrant does the point (1, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
40. 40.What is the distance between the points (1, 6) and (17, 18)? (a) 28 (b) 400 (c) 20 (d) 21

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