Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 417 · 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.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
2. 2.What is the midpoint of the line joining (0, 13) and (4, 7)? (a) (10, 2) (b) (4, 20) (c) (2, 3) (d) (2, 10)
3. 3.What is the midpoint of the line joining (10, 10) and (20, 14)? (a) (15, 12) (b) (30, 24) (c) (5, 2) (d) (12, 15)
4. 4.What is the midpoint of the line joining (8, 7) and (14, 11)? (a) (22, 18) (b) (9, 11) (c) (11, 9) (d) (3, 2)
5. 5.What is the midpoint of the line joining (7, 7) and (11, 5)? (a) (6, 9) (b) (18, 12) (c) (9, 6) (d) (2, 1)
6. 6.What is the midpoint of the line joining (1, 11) and (7, 5)? (a) (3, 3) (b) (4, 8) (c) (8, 16) (d) (8, 4)
7. 7.What is the distance between the points (2, 16) and (14, 7)? (a) 16 (b) 21 (c) 225 (d) 15
8. 8.What is the distance between the points (2, 7) and (14, 12)? (a) 17 (b) 14 (c) 169 (d) 13
9. 9.What is the distance between the points (1, 20) and (13, 4)? (a) 400 (b) 28 (c) 20 (d) 21
10. 10.What is the midpoint of the line joining (8, 10) and (10, 4)? (a) (1, 3) (b) (18, 14) (c) (9, 7) (d) (7, 9)
11. 11.What is the distance between the points (1, 4) and (16, 12)? (a) 18 (b) 289 (c) 23 (d) 17
12. 12.What is the distance between the points (2, 14) and (18, 2)? (a) 28 (b) 400 (c) 20 (d) 21
13. 13.What is the midpoint of the line joining (8, 0) and (14, 6)? (a) (3, 3) (b) (3, 11) (c) (11, 3) (d) (22, 6)
14. 14.What is the distance between the points (7, 16) and (31, 9)? (a) 26 (b) 625 (c) 25 (d) 31
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 (−9, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
18. 18.What is the midpoint of the line joining (2, 11) and (14, 7)? (a) (16, 18) (b) (6, 2) (c) (8, 9) (d) (9, 8)
19. 19.What is the midpoint of the line joining (10, 4) and (20, 12)? (a) (30, 16) (b) (5, 4) (c) (8, 15) (d) (15, 8)
20. 20.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
21. 21.What is the distance between the points (9, 9) and (25, 21)? (a) 28 (b) 21 (c) 400 (d) 20
22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
23. 23.In which quadrant does the point (−7, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
24. 24.What is the midpoint of the line joining (2, 7) and (12, 17)? (a) (14, 24) (b) (7, 12) (c) (12, 7) (d) (5, 5)
25. 25.What is the distance between the points (5, 2) and (17, 11)? (a) 15 (b) 225 (c) 21 (d) 16
26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
27. 27.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
28. 28.In which quadrant does the point (2, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
29. 29.What is the midpoint of the line joining (3, 1) and (13, 7)? (a) (16, 8) (b) (8, 4) (c) (4, 8) (d) (5, 3)
30. 30.In which quadrant does the point (−3, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
32. 32.In which quadrant does the point (2, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
33. 33.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
34. 34.In which quadrant does the point (2, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
36. 36.In which quadrant does the point (−5, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
37. 37.In which quadrant does the point (−9, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
38. 38.What is the distance between the points (0, 16) and (12, 0)? (a) 21 (b) 400 (c) 20 (d) 28
39. 39.What is the midpoint of the line joining (3, 6) and (7, 12)? (a) (10, 18) (b) (5, 9) (c) (2, 3) (d) (9, 5)
40. 40.What is the distance between the points (4, 3) and (7, 7)? (a) 7 (b) 25 (c) 5 (d) 6

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