Question

t is the midpoint of \\(\overline{ux}\\) and w is the midpoint of \\(\overline{vx}\\). if \\(uv = z\\) and \\(tw = 2z - 96\\), what is the value of \\(z\\)?

Explanation:

Step1: Apply Midsegment Theorem

$TW = \frac{1}{2}UV$

Step2: Substitute given values

$2z - 96 = \frac{1}{2}z$

Step3: Multiply by 2 to eliminate fraction

$2(2z - 96) = z \implies 4z - 192 = z$

Step4: Isolate z terms

$4z - z = 192 \implies 3z = 192$

Step5: Solve for z

$z = \frac{192}{3}$

Answer:

$64$