Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 78 · 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, 1) and (19, 9)? (a) 23 (b) 289 (c) 18 (d) 17
2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
4. 4.What is the midpoint of the line joining (0, 9) and (4, 1)? (a) (2, 4) (b) (4, 10) (c) (5, 2) (d) (2, 5)
5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
6. 6.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
8. 8.What is the midpoint of the line joining (9, 6) and (19, 2)? (a) (4, 14) (b) (28, 8) (c) (14, 4) (d) (5, 2)
9. 9.What is the midpoint of the line joining (4, 1) and (16, 7)? (a) (4, 10) (b) (10, 4) (c) (20, 8) (d) (6, 3)
10. 10.What is the midpoint of the line joining (10, 4) and (16, 6)? (a) (5, 13) (b) (26, 10) (c) (13, 5) (d) (3, 1)
11. 11.What is the distance between the points (7, 3) and (12, 15)? (a) 14 (b) 169 (c) 13 (d) 17
12. 12.What is the distance between the points (6, 0) and (9, 4)? (a) 6 (b) 7 (c) 5 (d) 25
13. 13.In which quadrant does the point (2, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
15. 15.In which quadrant does the point (−3, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
17. 17.What is the midpoint of the line joining (2, 5) and (14, 7)? (a) (16, 12) (b) (8, 6) (c) (6, 1) (d) (6, 8)
18. 18.What is the distance between the points (3, 7) and (27, 0)? (a) 625 (b) 25 (c) 26 (d) 31
19. 19.What is the distance between the points (0, 14) and (16, 2)? (a) 20 (b) 28 (c) 21 (d) 400
20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
22. 22.What is the distance between the points (1, 1) and (8, 25)? (a) 31 (b) 26 (c) 25 (d) 625
23. 23.What is the midpoint of the line joining (5, 2) and (9, 0)? (a) (2, 1) (b) (1, 7) (c) (14, 2) (d) (7, 1)
24. 24.In which quadrant does the point (8, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
25. 25.What is the midpoint of the line joining (0, 10) and (4, 0)? (a) (5, 2) (b) (3, 5) (c) (2, 5) (d) (4, 10)
26. 26.What is the distance between the points (7, 33) and (14, 9)? (a) 625 (b) 25 (c) 31 (d) 26
27. 27.What is the distance between the points (8, 1) and (13, 13)? (a) 14 (b) 169 (c) 17 (d) 13
28. 28.What is the midpoint of the line joining (6, 14) and (10, 10)? (a) (2, 2) (b) (12, 8) (c) (16, 24) (d) (8, 12)
29. 29.What is the distance between the points (5, 4) and (17, 20)? (a) 28 (b) 400 (c) 21 (d) 20
30. 30.What is the distance between the points (1, 13) and (9, 7)? (a) 10 (b) 14 (c) 100 (d) 11
31. 31.What is the midpoint of the line joining (1, 16) and (5, 6)? (a) (3, 11) (b) (11, 3) (c) (2, 5) (d) (6, 22)
32. 32.What is the midpoint of the line joining (4, 4) and (8, 14)? (a) (12, 18) (b) (9, 6) (c) (6, 9) (d) (2, 5)
33. 33.In which quadrant does the point (9, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
34. 34.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (8, 10) and (10, 4)? (a) (7, 9) (b) (1, 3) (c) (18, 14) (d) (9, 7)
36. 36.What is the midpoint of the line joining (0, 12) and (12, 10)? (a) (6, 1) (b) (11, 6) (c) (12, 22) (d) (6, 11)
37. 37.What is the distance between the points (6, 0) and (12, 8)? (a) 100 (b) 14 (c) 11 (d) 10
38. 38.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
39. 39.What is the distance between the points (6, 10) and (18, 1)? (a) 225 (b) 16 (c) 15 (d) 21
40. 40.What is the distance between the points (8, 3) and (12, 0)? (a) 7 (b) 5 (c) 6 (d) 25

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