Final answer:
Calculating the length of PM in triangle LTM, with XY being the perpendicular bisector of TM (6 cm), and given TP is 5 cm, the correct length of PM is 1 cm; however, this answer isn't provided in the options.
Step-by-step explanation:
The question asks for the length of the segment PM in a triangle LTM, where XY is the perpendicular bisector of TM. Given that the full length of TM is 6 centimeters, and that TP is a segment of TM with a length of 5 centimeters, we can determine the length of PM as follows:
- Understand that since XY bisects TM, it divides TM into two equal lengths, meaning each of these lengths is half of TM's total length.
- Calculate the length of each section as 6 cm / 2 = 3 cm.
- Since TP is a 5 cm segment of TM, TP + PM equals the total length of TM, which is 6 cm.
- Therefore, the length of PM is 6 cm - 5 cm = 1 cm.
However, the provided options do not include 1 cm, which may indicate that there's been an error in either the question or the available options. Among the available answers, option (a) 2.5 centimeters is the closest to half of TM, but this doesn’t correspond to the correct calculation based on the information given.