At 5 AM one day, a monk be- gan a trek from his monastery by the sea to the monastery at the top of a mountain. He reached the mountain-top monastery at 11 AM, spent the rest of the day in meditation, and then slept the night there. In the morning, at 5 AM, he began walking back to the seaside monastery. Though walking downhill should have been faster, he dawdled in the beautiful sunshine, and ending up getting to the seaside monastery at exactly 11 AM.

(a) trip when the monk was in exactly the same place on both days? Why or why not?

(b) Suppose the monk walked faster on the second day, and got back at 9 AM. What is your answer to part (a) in this case?

(c) Suppose the monk started later, at 10 AM, and reached the seaside monastery at 3 PM. What is your answer to part (a) in this case?

(a) Yes

(b) No

(c) No

Step-by-step explanation:

(a) Yes

Due to the fact that the monk started at both the journeys at the same time, and completed both journeys at the same time, there is a likelihood that the monk was at the middle of the journey at about the same time of half the journey's duration

(b) Where the monk started the journey back at 5 AM and completed, got back at 9 AM, then it is unlikely that the monk would ave been at the same time because the distance covered per unit time is different while the starting time is the same

(c) Here we have the the start time as 10 AM and the arrival at the seaside monastery at 3 PM, therefore, to answer the  question, we assume another monk start from the seaside monastery at 5 AM on a journey to the mpnstery at the top of the mountain, to arrive there by 11 AM, since the time difference for both journeys are

11 AM - 5 AM = 6 Hours and

3 PM  - 10 AM = 5 Hours

The midpoint of the journey will therefore be reached at different times by the two monks

Time to mid point for monk 1 = 6/2 or 3 hours

Time to mid point for monk 2 = 5/2 or 2.5 hours.

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)