Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 944 · 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 midpoint of the line joining (1, 0) and (5, 6)? (a) (3, 3) (b) (4, 3) (c) (2, 3) (d) (6, 6)
2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
3. 3.In which quadrant does the point (−6, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
4. 4.What is the midpoint of the line joining (8, 13) and (14, 9)? (a) (3, 2) (b) (12, 11) (c) (22, 22) (d) (11, 11)
5. 5.What is the distance between the points (9, 15) and (21, 6)? (a) 15 (b) 21 (c) 225 (d) 16
6. 6.What is the distance between the points (9, 4) and (21, 20)? (a) 28 (b) 400 (c) 20 (d) 21
7. 7.In which quadrant does the point (−3, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
8. 8.What is the distance between the points (1, 14) and (16, 6)? (a) 18 (b) 17 (c) 23 (d) 289
9. 9.What is the distance between the points (8, 1) and (15, 25)? (a) 625 (b) 31 (c) 26 (d) 25
10. 10.What is the midpoint of the line joining (6, 12) and (10, 10)? (a) (11, 8) (b) (2, 1) (c) (16, 22) (d) (8, 11)
11. 11.What is the midpoint of the line joining (10, 8) and (14, 14)? (a) (12, 11) (b) (11, 12) (c) (2, 3) (d) (24, 22)
12. 12.What is the midpoint of the line joining (10, 1) and (12, 7)? (a) (22, 8) (b) (1, 3) (c) (4, 11) (d) (11, 4)
13. 13.In which quadrant does the point (5, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
15. 15.What is the midpoint of the line joining (1, 6) and (5, 0)? (a) (4, 3) (b) (3, 3) (c) (6, 6) (d) (2, 3)
16. 16.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
17. 17.What is the midpoint of the line joining (9, 18) and (21, 10)? (a) (15, 14) (b) (6, 4) (c) (14, 15) (d) (30, 28)
18. 18.What is the distance between the points (2, 8) and (6, 11)? (a) 7 (b) 5 (c) 25 (d) 6
19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
20. 20.In which quadrant does the point (4, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
21. 21.What is the distance between the points (8, 9) and (20, 4)? (a) 17 (b) 13 (c) 14 (d) 169
22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
23. 23.What is the midpoint of the line joining (8, 20) and (10, 10)? (a) (9, 15) (b) (1, 5) (c) (15, 9) (d) (18, 30)
24. 24.What is the midpoint of the line joining (9, 14) and (19, 10)? (a) (28, 24) (b) (14, 12) (c) (5, 2) (d) (12, 14)
25. 25.What is the distance between the points (1, 9) and (13, 14)? (a) 169 (b) 14 (c) 17 (d) 13
26. 26.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
27. 27.What is the distance between the points (0, 8) and (8, 23)? (a) 18 (b) 289 (c) 23 (d) 17
28. 28.In which quadrant does the point (9, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
29. 29.What is the distance between the points (9, 7) and (17, 22)? (a) 289 (b) 18 (c) 23 (d) 17
30. 30.What is the midpoint of the line joining (6, 6) and (12, 12)? (a) (18, 18) (b) (9, 9) (c) (10, 9) (d) (3, 3)
31. 31.What is the distance between the points (6, 25) and (18, 9)? (a) 28 (b) 400 (c) 21 (d) 20
32. 32.What is the midpoint of the line joining (9, 6) and (13, 4)? (a) (11, 5) (b) (2, 1) (c) (5, 11) (d) (22, 10)
33. 33.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
34. 34.What is the midpoint of the line joining (9, 3) and (17, 15)? (a) (4, 6) (b) (9, 13) (c) (13, 9) (d) (26, 18)
35. 35.What is the distance between the points (2, 9) and (26, 2)? (a) 625 (b) 25 (c) 31 (d) 26
36. 36.What is the distance between the points (2, 0) and (14, 5)? (a) 169 (b) 13 (c) 17 (d) 14
37. 37.What is the distance between the points (9, 6) and (16, 30)? (a) 25 (b) 26 (c) 625 (d) 31
38. 38.What is the distance between the points (7, 5) and (19, 0)? (a) 13 (b) 169 (c) 14 (d) 17
39. 39.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
40. 40.What is the distance between the points (3, 8) and (7, 11)? (a) 6 (b) 5 (c) 7 (d) 25

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