Question

t is the midpoint of \\(\overline{su}\\). if \\(st = x + 8\\) and \\(tu = 2x - 1\\), what is \\(tu\\)?

s

t

u

simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Set ST equal to TU (midpoint property)

Since T is the midpoint of \(\overline{SU}\), \(ST = TU\). So we set up the equation: \(x + 8 = 2x - 1\)

Step2: Solve for x

Subtract \(x\) from both sides: \(8 = x - 1\)
Then add 1 to both sides: \(x = 9\)

Step3: Find TU by substituting x

Substitute \(x = 9\) into the expression for \(TU\) (\(TU = 2x - 1\)): \(TU = 2(9) - 1 = 18 - 1 = 17\)

Answer:

17