Find the co-ordinates of the points of trisection of the straight line joining…
2019
Find the co-ordinates of the points of trisection of the straight line joining the points A(1, −2) and B(−3, 4).
- A.
(5/3, −2) & (1/3, 0)
- B.
(−5/3, 2) & (1/3, 0)
- C.
(5/3, 2) & (1/3, 0)
- D.
(−5/3, 2) & (−1/3, 0)
Attempted by 33 students.
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Correct answer: D
Method: Find vector AB and take one-third and two-thirds of it from A.
Compute AB = B − A = (−3 − 1, 4 − (−2)) = (−4, 6).
First trisection point (one-third from A): A + (1/3)AB = (1 + (1/3)(−4), −2 + (1/3)(6)) = (−1/3, 0).
Second trisection point (two-thirds from A): A + (2/3)AB = (1 + (2/3)(−4), −2 + (2/3)(6)) = (−5/3, 2).
Answer: The points of trisection are (−1/3, 0) and (−5/3, 2).
Note: The order can be listed in either order; the two required points are (−1/3, 0) and (−5/3, 2).
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