Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 526 · 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 distance between the points (4, 13) and (12, 7)? (a) 10 (b) 14 (c) 11 (d) 100
2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
3. 3.In which quadrant does the point (3, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
4. 4.What is the midpoint of the line joining (0, 7) and (6, 9)? (a) (8, 3) (b) (6, 16) (c) (3, 1) (d) (3, 8)
5. 5.What is the distance between the points (7, 13) and (19, 8)? (a) 14 (b) 13 (c) 169 (d) 17
6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
7. 7.What is the midpoint of the line joining (0, 13) and (2, 5)? (a) (2, 18) (b) (9, 1) (c) (1, 9) (d) (1, 4)
8. 8.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
9. 9.In which quadrant does the point (2, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
10. 10.What is the midpoint of the line joining (7, 0) and (19, 6)? (a) (3, 13) (b) (6, 3) (c) (13, 3) (d) (26, 6)
11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
13. 13.What is the midpoint of the line joining (6, 2) and (18, 4)? (a) (24, 6) (b) (3, 12) (c) (6, 1) (d) (12, 3)
14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
15. 15.What is the distance between the points (7, 4) and (19, 9)? (a) 169 (b) 14 (c) 17 (d) 13
16. 16.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
17. 17.What is the midpoint of the line joining (10, 6) and (22, 0)? (a) (32, 6) (b) (3, 16) (c) (6, 3) (d) (16, 3)
18. 18.What is the distance between the points (3, 3) and (19, 15)? (a) 28 (b) 400 (c) 20 (d) 21
19. 19.What is the distance between the points (5, 1) and (11, 9)? (a) 11 (b) 14 (c) 100 (d) 10
20. 20.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
21. 21.What is the midpoint of the line joining (2, 0) and (6, 10)? (a) (5, 4) (b) (2, 5) (c) (8, 10) (d) (4, 5)
22. 22.What is the midpoint of the line joining (1, 6) and (3, 0)? (a) (1, 3) (b) (2, 3) (c) (3, 2) (d) (4, 6)
23. 23.What is the distance between the points (4, 18) and (13, 6)? (a) 16 (b) 15 (c) 225 (d) 21
24. 24.In which quadrant does the point (−9, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
25. 25.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
27. 27.What is the distance between the points (9, 6) and (17, 12)? (a) 11 (b) 10 (c) 100 (d) 14
28. 28.What is the distance between the points (4, 15) and (20, 3)? (a) 400 (b) 28 (c) 21 (d) 20
29. 29.In which quadrant does the point (5, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
30. 30.What is the distance between the points (4, 9) and (28, 16)? (a) 31 (b) 625 (c) 26 (d) 25
31. 31.What is the distance between the points (0, 0) and (8, 6)? (a) 10 (b) 100 (c) 14 (d) 11
32. 32.What is the midpoint of the line joining (3, 14) and (11, 2)? (a) (8, 7) (b) (4, 6) (c) (7, 8) (d) (14, 16)
33. 33.What is the distance between the points (5, 18) and (10, 6)? (a) 14 (b) 17 (c) 169 (d) 13
34. 34.In which quadrant does the point (2, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (7, 1) and (9, 5)? (a) (1, 2) (b) (8, 3) (c) (16, 6) (d) (3, 8)
36. 36.What is the distance between the points (5, 5) and (17, 10)? (a) 169 (b) 14 (c) 13 (d) 17
37. 37.In which quadrant does the point (−5, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
38. 38.What is the distance between the points (9, 2) and (14, 14)? (a) 169 (b) 17 (c) 13 (d) 14
39. 39.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
40. 40.What is the midpoint of the line joining (7, 6) and (15, 10)? (a) (8, 11) (b) (4, 2) (c) (22, 16) (d) (11, 8)

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