Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 748 · 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) 18 (b) 17 (c) 289 (d) 23
2. 2.What is the midpoint of the line joining (1, 7) and (7, 9)? (a) (8, 16) (b) (4, 8) (c) (3, 1) (d) (8, 4)
3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
4. 4.What is the distance between the points (4, 8) and (16, 24)? (a) 21 (b) 400 (c) 20 (d) 28
5. 5.What is the midpoint of the line joining (4, 3) and (10, 13)? (a) (8, 7) (b) (3, 5) (c) (14, 16) (d) (7, 8)
6. 6.What is the midpoint of the line joining (10, 19) and (20, 7)? (a) (13, 15) (b) (5, 6) (c) (30, 26) (d) (15, 13)
7. 7.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
8. 8.What is the distance between the points (0, 17) and (12, 1)? (a) 400 (b) 21 (c) 20 (d) 28
9. 9.What is the midpoint of the line joining (0, 17) and (12, 7)? (a) (12, 24) (b) (6, 12) (c) (6, 5) (d) (12, 6)
10. 10.What is the distance between the points (3, 17) and (8, 5)? (a) 169 (b) 14 (c) 17 (d) 13
11. 11.What is the distance between the points (0, 2) and (3, 6)? (a) 7 (b) 6 (c) 5 (d) 25
12. 12.What is the distance between the points (1, 7) and (13, 2)? (a) 14 (b) 169 (c) 13 (d) 17
13. 13.What is the distance between the points (2, 9) and (14, 25)? (a) 28 (b) 21 (c) 20 (d) 400
14. 14.What is the midpoint of the line joining (5, 5) and (9, 15)? (a) (10, 7) (b) (2, 5) (c) (14, 20) (d) (7, 10)
15. 15.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
16. 16.What is the distance between the points (6, 29) and (13, 5)? (a) 26 (b) 31 (c) 625 (d) 25
17. 17.What is the midpoint of the line joining (6, 1) and (8, 3)? (a) (1, 1) (b) (2, 7) (c) (7, 2) (d) (14, 4)
18. 18.In which quadrant does the point (−5, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
20. 20.In which quadrant does the point (3, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
21. 21.What is the midpoint of the line joining (8, 11) and (14, 3)? (a) (7, 11) (b) (3, 4) (c) (22, 14) (d) (11, 7)
22. 22.What is the distance between the points (2, 4) and (26, 11)? (a) 25 (b) 26 (c) 31 (d) 625
23. 23.What is the distance between the points (1, 3) and (5, 6)? (a) 25 (b) 5 (c) 6 (d) 7
24. 24.What is the midpoint of the line joining (10, 12) and (14, 2)? (a) (12, 7) (b) (24, 14) (c) (2, 5) (d) (7, 12)
25. 25.What is the midpoint of the line joining (6, 11) and (8, 5)? (a) (8, 7) (b) (1, 3) (c) (14, 16) (d) (7, 8)
26. 26.What is the midpoint of the line joining (2, 5) and (4, 3)? (a) (4, 3) (b) (3, 4) (c) (1, 1) (d) (6, 8)
27. 27.What is the distance between the points (5, 3) and (9, 0)? (a) 6 (b) 25 (c) 5 (d) 7
28. 28.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
29. 29.In which quadrant does the point (−2, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
30. 30.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
31. 31.In which quadrant does the point (6, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
32. 32.What is the distance between the points (2, 2) and (8, 10)? (a) 10 (b) 14 (c) 11 (d) 100
33. 33.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
34. 34.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
35. 35.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.What is the distance between the points (8, 12) and (24, 0)? (a) 400 (b) 28 (c) 21 (d) 20
37. 37.What is the midpoint of the line joining (0, 14) and (4, 10)? (a) (12, 2) (b) (2, 2) (c) (4, 24) (d) (2, 12)
38. 38.What is the midpoint of the line joining (6, 3) and (16, 13)? (a) (5, 5) (b) (8, 11) (c) (11, 8) (d) (22, 16)
39. 39.What is the distance between the points (2, 8) and (10, 23)? (a) 18 (b) 17 (c) 23 (d) 289
40. 40.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant

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