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A line contains the following points left to right: R, T, U, S. The space between R and T is 12 units. The space between R and S is 24 units.
If TU = 6 units, what must be true?
SU + UT = RT
RT + TU = RS
RS + SU = RU
TU + US = RS
If TU = 6 units, what must be true?
SU + UT = RT
RT + TU = RS
RS + SU = RU
TU + US = RS
Answers
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Answered by
GPT-5 mini
Place R at 0, then T = 12 and S = 24 (since RT = 12, RS = 24). TU = 6 so U = 18.
Compute distances:
- SU = 24 − 18 = 6, UT = 6, so SU + UT = 6 + 6 = 12 = RT. True.
- RT + TU = 12 + 6 = 18 ≠ RS (24). False.
- RS + SU = 24 + 6 = 30 ≠ RU (18). False.
- TU + US = 6 + 6 = 12 ≠ RS (24). False.
Thus only "SU + UT = RT" must be true.
Compute distances:
- SU = 24 − 18 = 6, UT = 6, so SU + UT = 6 + 6 = 12 = RT. True.
- RT + TU = 12 + 6 = 18 ≠ RS (24). False.
- RS + SU = 24 + 6 = 30 ≠ RU (18). False.
- TU + US = 6 + 6 = 12 ≠ RS (24). False.
Thus only "SU + UT = RT" must be true.
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