Final answer:
The correct answer is d. The sum of the distances from U to V and U to T, as U is the midpoint, making VU and UT equal, representing the full length of segment TV.
Step-by-step explanation:
To determine how far you need to travel to drive home from your grandma's house if U is the midpoint of segment TV, you need to consider the definition of a midpoint. The midpoint of a line segment is the exact middle point, which divides the segment into two equal parts. Therefore, if U is the midpoint, then the distance from T to U is equal to the distance from U to V. Since you are starting at your grandma's house at point V and going to your house at point T, the full distance you need to travel is the length of segment TV, which is twice the distance from V to U (since VU = UT).
Given the options provided:
- a. Half the distance from V to T is the distance from V to U, but we need to travel the full distance from V to T.
- b. The distance from T to U is equal to the distance from V to U, but still only half of the total distance we need to travel.
- c. The distance from V to U is equal to the distance from U to T, which is half of the full distance from V to T.
- d. The sum of the distances from U to V and U to T is the correct choice since it represents the full length of segment TV, which is the distance from your grandma's house to your house