Coordinate Geometry Worksheet for Maths Olympiad

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

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