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