Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 983 · 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, 5) and (13, 3)? (a) (6, 1) (b) (4, 7) (c) (14, 8) (d) (7, 4)
2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
3. 3.What is the distance between the points (3, 11) and (6, 7)? (a) 7 (b) 6 (c) 5 (d) 25
4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
6. 6.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
7. 7.In which quadrant does the point (−5, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
8. 8.In which quadrant does the point (6, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
9. 9.In which quadrant does the point (6, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
10. 10.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
11. 11.What is the midpoint of the line joining (9, 4) and (15, 8)? (a) (12, 6) (b) (6, 12) (c) (3, 2) (d) (24, 12)
12. 12.What is the distance between the points (8, 4) and (12, 1)? (a) 5 (b) 25 (c) 7 (d) 6
13. 13.What is the midpoint of the line joining (3, 3) and (9, 1)? (a) (12, 4) (b) (3, 1) (c) (2, 6) (d) (6, 2)
14. 14.What is the midpoint of the line joining (7, 13) and (17, 3)? (a) (12, 8) (b) (5, 5) (c) (8, 12) (d) (24, 16)
15. 15.What is the midpoint of the line joining (4, 0) and (16, 6)? (a) (3, 10) (b) (10, 3) (c) (6, 3) (d) (20, 6)
16. 16.What is the midpoint of the line joining (8, 9) and (16, 13)? (a) (11, 12) (b) (4, 2) (c) (12, 11) (d) (24, 22)
17. 17.What is the midpoint of the line joining (6, 10) and (16, 12)? (a) (22, 22) (b) (5, 1) (c) (12, 11) (d) (11, 11)
18. 18.In which quadrant does the point (−8, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
19. 19.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
20. 20.What is the distance between the points (3, 14) and (15, 9)? (a) 169 (b) 14 (c) 17 (d) 13
21. 21.What is the midpoint of the line joining (9, 21) and (11, 9)? (a) (1, 6) (b) (15, 10) (c) (10, 15) (d) (20, 30)
22. 22.What is the distance between the points (4, 33) and (11, 9)? (a) 26 (b) 31 (c) 25 (d) 625
23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
24. 24.In which quadrant does the point (6, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
25. 25.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
26. 26.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
27. 27.What is the midpoint of the line joining (4, 9) and (6, 5)? (a) (10, 14) (b) (7, 5) (c) (1, 2) (d) (5, 7)
28. 28.What is the distance between the points (4, 6) and (8, 9)? (a) 5 (b) 7 (c) 6 (d) 25
29. 29.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
30. 30.What is the distance between the points (0, 0) and (4, 3)? (a) 6 (b) 5 (c) 7 (d) 25
31. 31.What is the distance between the points (2, 7) and (14, 12)? (a) 17 (b) 169 (c) 13 (d) 14
32. 32.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
33. 33.What is the distance between the points (6, 1) and (9, 5)? (a) 7 (b) 6 (c) 5 (d) 25
34. 34.What is the midpoint of the line joining (2, 12) and (6, 4)? (a) (2, 4) (b) (8, 16) (c) (4, 8) (d) (8, 4)
35. 35.What is the midpoint of the line joining (4, 5) and (14, 7)? (a) (18, 12) (b) (5, 1) (c) (9, 6) (d) (6, 9)
36. 36.What is the distance between the points (5, 14) and (20, 6)? (a) 289 (b) 18 (c) 23 (d) 17
37. 37.What is the distance between the points (0, 9) and (24, 2)? (a) 31 (b) 625 (c) 26 (d) 25
38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
39. 39.What is the midpoint of the line joining (9, 22) and (13, 10)? (a) (22, 32) (b) (2, 6) (c) (11, 16) (d) (16, 11)
40. 40.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15

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