Final answer:
The measure of T'U' after dilating TU by a scale factor of 1/3 is 5 units.
Step-by-step explanation:
When a segment TU is dilated by a scale factor of 1/3 to form T'U', the length of T'U' is obtained by multiplying the length of TU by the scale factor. Since TU measures 15, we apply the scale factor as follows:
T'U' = TU × scale factor
T'U' = 15 × 1/3
T'U' = 5
So, the measure of T'U' after the dilation is 5.