Final answer:
The length of TU is 2 units.
Step-by-step explanation:
To find the length of TU with a given slope of -(5)/(2), we can use the formula for the slope of a line, which is represented as m = (change in y)/(change in x). In this case, the slope is -(5)/(2), which means for every 2 units of change in x, there is a corresponding change of 5 units in y. Since the slope is negative, the line is decreasing.
Now, we can use the Pythagorean Theorem to find the length of TU. Considering the change in x as the base and the change in y as the height, the length TU can be calculated as the square root of the sum of the squares of the base and height. Using the values derived from the slope, the length TU is found to be 2 units.
In summary, the length of TU is determined by understanding the relationship between the slope and the changes in x and y. The Pythagorean Theorem is then applied to find the length of the line segment TU, resulting in a final answer of 2 units.