Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 603 · 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 (10, 14) and (18, 10)? (a) (28, 24) (b) (12, 14) (c) (14, 12) (d) (4, 2)
2. 2.What is the distance between the points (0, 7) and (3, 11)? (a) 5 (b) 25 (c) 6 (d) 7
3. 3.What is the midpoint of the line joining (0, 10) and (2, 0)? (a) (2, 10) (b) (5, 1) (c) (1, 5) (d) (2, 5)
4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
5. 5.What is the midpoint of the line joining (6, 3) and (10, 7)? (a) (5, 8) (b) (2, 2) (c) (16, 10) (d) (8, 5)
6. 6.In which quadrant does the point (−4, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
7. 7.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
9. 9.In which quadrant does the point (3, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
10. 10.What is the distance between the points (0, 0) and (24, 7)? (a) 625 (b) 31 (c) 25 (d) 26
11. 11.In which quadrant does the point (4, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
12. 12.What is the distance between the points (6, 6) and (15, 18)? (a) 21 (b) 15 (c) 225 (d) 16
13. 13.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
14. 14.What is the midpoint of the line joining (6, 21) and (10, 9)? (a) (2, 6) (b) (15, 8) (c) (8, 15) (d) (16, 30)
15. 15.What is the distance between the points (3, 5) and (6, 1)? (a) 7 (b) 6 (c) 25 (d) 5
16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
17. 17.What is the distance between the points (4, 0) and (12, 15)? (a) 17 (b) 289 (c) 23 (d) 18
18. 18.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
19. 19.What is the distance between the points (4, 8) and (28, 1)? (a) 31 (b) 25 (c) 625 (d) 26
20. 20.What is the distance between the points (5, 2) and (17, 11)? (a) 225 (b) 21 (c) 16 (d) 15
21. 21.What is the distance between the points (8, 12) and (24, 0)? (a) 21 (b) 400 (c) 28 (d) 20
22. 22.In which quadrant does the point (−8, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (−8, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
24. 24.In which quadrant does the point (−9, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
25. 25.What is the midpoint of the line joining (7, 3) and (9, 5)? (a) (4, 8) (b) (1, 1) (c) (8, 4) (d) (16, 8)
26. 26.What is the distance between the points (5, 12) and (13, 6)? (a) 14 (b) 10 (c) 11 (d) 100
27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
28. 28.In which quadrant does the point (8, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
29. 29.In which quadrant does the point (3, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
30. 30.What is the distance between the points (6, 5) and (11, 17)? (a) 14 (b) 13 (c) 17 (d) 169
31. 31.What is the distance between the points (0, 19) and (5, 7)? (a) 14 (b) 13 (c) 169 (d) 17
32. 32.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
33. 33.What is the distance between the points (9, 3) and (24, 11)? (a) 289 (b) 17 (c) 23 (d) 18
34. 34.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
35. 35.In which quadrant does the point (−6, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
36. 36.What is the midpoint of the line joining (2, 6) and (12, 12)? (a) (9, 7) (b) (14, 18) (c) (5, 3) (d) (7, 9)
37. 37.What is the midpoint of the line joining (0, 5) and (10, 17)? (a) (5, 6) (b) (5, 11) (c) (11, 5) (d) (10, 22)
38. 38.What is the midpoint of the line joining (3, 10) and (15, 12)? (a) (18, 22) (b) (6, 1) (c) (9, 11) (d) (11, 9)
39. 39.What is the distance between the points (5, 6) and (9, 9)? (a) 6 (b) 25 (c) 5 (d) 7
40. 40.What is the distance between the points (1, 15) and (10, 3)? (a) 16 (b) 225 (c) 21 (d) 15

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