Question

Исполнителю чертежник был дан алгоритм: повтори 3 раза. сместиться на вектор (-1,-2) сместиться на вектор (4,-2) конец. Определите исходную точку чертежника если после выполнения команд он оказался в точке(11,-8). Пожалуйста помогите))))

Answer 1

Algorithm Analysis

The given algorithm instructs the drafter to perform a series of commands three times. The commands are as follows: 1. Move in the direction of the vector (-1, -2). 2. Move in the direction of the vector (4, -2).

The goal is to determine the initial position of the drafter if, after executing these commands, they end up at the point (11, -8).

Solution

To solve this problem, we need to reverse the steps taken by the drafter to find their initial position. Let's go step by step:

1. Move in the direction of the vector (-1, -2): - To reverse this step, we need to move in the opposite direction, which is (1, 2). - So, the drafter's position after this step is (11 + 1, -8 + 2) = (12, -6).

2. Move in the direction of the vector (4, -2): - To reverse this step, we need to move in the opposite direction, which is (-4, 2). - So, the drafter's position after this step is (12 - 4, -6 + 2) = (8, -4).

3. Repeat steps 1 and 2 two more times: - After repeating the steps twice, the drafter's position will be: - (8 + 1 + 1, -4 + 2 + 2) = (10, 0) after the first repetition. - (10 + 1 + 1, 0 + 2 + 2) = (12, 4) after the second repetition.

Therefore, the initial position of the drafter is (12, 4).

Please let me know if you need any further assistance!