Coordinates and trigonometry · Ages 14–15
The mid-point formula worksheet
Part of: Coordinate geometry
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The mid-point formula worksheet
Coordinates and trigonometry · Ages 14–15
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.The mid-point of A(−4, 0) and B(0, 2) is M = (, ).
Fill in each blank
Answer:
2.The mid-point of A(5, 2) and B(7, 6) is M = (, ).
Fill in each blank
Answer:
3.The segment AB has one end at A(2, 4) and its mid-point at M(−4, −6). The other end is B = (, ).
Fill in each blank
Answer:
4.Read A and B off the picture. The mid-point of AB is (, ).
Fill in each blank
Answer:
5.The segment AB has one end at A(4, 5) and its mid-point at M(−2, 6). The other end is B = (, ).
Fill in each blank
Answer:
6.The mid-point of A(−5, −3) and B(−8, −5) has x-coordinate (as a fraction)
Answer in simplest form
Answer:
7.Going from A(2, −3) to B(−4, 1), x changes by and y by . The mid-point is half the way, so it is (, ).
Fill in each blank
Answer:
8.Going from A(5, 6) to B(−3, 0), x changes by and y by . The mid-point is half the way, so it is (, ).
Fill in each blank
Answer:
9.The mid-point of A(6, 8) and B(5, 0) has x-coordinate (as a fraction)
Answer in simplest form
Answer:
Part B: Choose, or true or false (2 marks each)
10.The segment AB runs from A(−1, −5) to B(1, −3). Which point is its mid-point?
- A. (1, 1)
- B. (−4, 0)
- C. (0, −4)
- D. (0, −8)
Choose the right answer
Answer:
11.M(2, −1) is the mid-point of A(3, −5) and B(1, 3).
True or false?
Answer:
12.M(−5, −1) is the mid-point of A(−4, 1) and B(−6, −3).
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A park path runs straight from A(−5, −6) to B(−3, −2), with a fountain at its mid-point and a shelter at C(−16, 1), each unit 1 m. The fountain is at (, ), and it is m in a straight line to the shelter.
Fill in each blank
Working:
Answer:
14.A straight cycle path starts at A(5, 2), and the rest stop M(−6, −4) is exactly at its mid-point. The path ends at (, ).
Fill in each blank
Working:
Answer:
15.On a floor plan, a diameter of a round table runs from A(3, −2) to B(−9, −18), each unit 10 cm. The centre is at (, ), and the radius is units.
Fill in each blank
Working:
Answer:
16.Two friends live at A(−2, 7) and B(2, 3) and agree to meet at the mid-point of the line between their homes. They meet at (, ).
Fill in each blank
Working:
Answer:
17.A straight cycle path starts at A(−5, 3), and the rest stop M(6, 6) is exactly at its mid-point. The path ends at (, ).
Fill in each blank
Working:
Answer:
18.A park path runs straight from A(−4, −1) to B(2, 5), with a fountain at its mid-point and a shelter at C(7, 8), each unit 1 m. The fountain is at (, ), and it is m in a straight line to the shelter.
Fill in each blank
Working:
Answer:
Show the answers and working
The mid-point formula worksheet: Answers and working
Part A: Working out and filling in
1. −2, 1
The mid-point averages the ends: (−4 + (0)2, 0 + (2)2) = (−42, 22) = (−2, 1).
2. 6, 4
The mid-point averages the ends: (5 + (7)2, 2 + (6)2) = (122, 82) = (6, 4).
3. −10, −16
2 + x2 = −4, so x = 2 × (−4) − (2) = −8 − (2) = −10; likewise y = −12 − (4) = −16. As far again from M as from A to M.
4. −1, 3
A(−4, 5) and B(2, 1): the mid-point is (−4 + (2)2, 5 + (1)2) = (−1, 3).
5. −8, 7
4 + x2 = −2, so x = 2 × (−2) − (4) = −4 − (4) = −8; likewise y = 12 − (5) = 7. As far again from M as from A to M.
6. −132
x = −5 + (−8)2 = −132: it doesn't come out whole, so it is the fraction −132.
7. −6, 4, −1, −1
x changes by −6, half is −3: 2 + (−3) = −1; y by 4, half 2: −3 + (2) = −1. The same as the averages, (2 + (−4)2, …).
8. −8, −6, 1, 3
x changes by −8, half is −4: 5 + (−4) = 1; y by −6, half −3: 6 + (−3) = 3. The same as the averages, (5 + (−3)2, …).
9. 112
x = 6 + (5)2 = 112: it doesn't come out whole, so it is the fraction 112.
Part B: Choose, or true or false
10. C. (0, −4)
M = (−1 + (1)2, −5 + (−3)2) = (0, −4).
11. True
The mid-point is (3 + (1)2, −5 + (3)2) = (2, −1).
12. True
The mid-point is (−4 + (−6)2, 1 + (−3)2) = (−5, −1).
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. −4, −4, 13
The fountain is at (−5 + (−3)2, −6 + (−2)2) = (−4, −4); to C is 12 across and 5 up or down, 122 + 52 = 13 m.
14. −17, −10
Walk from M as A walked to M: (2 × (−6) − (5), 2 × (−4) − (2)) = (−17, −10).
15. −3, −10, 10
The centre is the diameter's mid-point: (3 + (−9)2, −2 + (−18)2) = (−3, −10); the diameter AB is 20, so the radius is 10.
16. 0, 5
The mid-point is (−2 + (2)2, 7 + (3)2) = (0, 5).
17. 17, 9
Walk from M as A walked to M: (2 × (6) − (−5), 2 × (6) − (3)) = (17, 9).
18. −1, 2, 10
The fountain is at (−4 + (2)2, −1 + (5)2) = (−1, 2); to C is 8 across and 6 up or down, 82 + 62 = 10 m.
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