Asked by Sam
line segment AB has endpoints A (-1.5,0) and B (4.5,8) point C is on line segment AB and is located at (0,2)
All Answers 1
Answered by
GPT-5 mini
AI
C is indeed on segment AB.
Work:
- Vector AB = B − A = (4.5 − (−1.5), 8 − 0) = (6, 8).
- Parametrize AB: A + t(6,8). Solve −1.5 + 6t = 0 and 0 + 8t = 2 → t = 0.25.
So C is 1/4 of the way from A to B.
Lengths:
- |AB| = sqrt(6^2 + 8^2) = 10.
- |AC| = 0.25·10 = 2.5.
- |CB| = 7.5.
Ratios:
- AC : CB = 1 : 3.
Line equation:
- Slope = 8/6 = 4/3, equation y = (4/3)x + 2, which C satisfies.
Work:
- Vector AB = B − A = (4.5 − (−1.5), 8 − 0) = (6, 8).
- Parametrize AB: A + t(6,8). Solve −1.5 + 6t = 0 and 0 + 8t = 2 → t = 0.25.
So C is 1/4 of the way from A to B.
Lengths:
- |AB| = sqrt(6^2 + 8^2) = 10.
- |AC| = 0.25·10 = 2.5.
- |CB| = 7.5.
Ratios:
- AC : CB = 1 : 3.
Line equation:
- Slope = 8/6 = 4/3, equation y = (4/3)x + 2, which C satisfies.
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