To solve this problem, we need to visualize the path Rajat takes and then calculate the distance between points P and Q.

1. Rajat starts at point P and walks 5m north.

2. He then takes a right turn and walks 4m. At this point, he is 5m north and 4m east of point P.

3. Next, he takes a left turn and walks 4m. Now, he is 5m north and 4m west of his previous position, which means he is 1m west of point P.

4. Then, he turns 135° anti-clockwise. This direction is southwest if we consider north as 0°.

5. He walks 4√2 m in the southwest direction. This distance will be split equally between south and west due to the 45° angle of southwest. So, he walks 4m west and 4m south.

6. Now, he is 4m south and 5m west of point P.

To find the distance between points P and Q, we can use the Pythagorean theorem because the path forms a right triangle. The theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, the distance between P and Q = √((4m)^2 + (5m)^2) = √(16m^2 + 25m^2) = √41m^2 = approximately 6.4m.

Therefore, the distance between points P and Q is more than 6 meters.

Question

To solve this problem, we need to visualize the path Rajat takes and then calculate the distance between points P and Q.

1. Rajat starts at point P and walks 5m north.

2. He then takes a right turn and walks 4m. At this point, he is 5m north and 4m east of point P.

3. Next, he takes a left turn and walks 4m. Now, he is 5m north and 4m west of his previous position, which means he is 1m west of point P.

4. Then, he turns 135° anti-clockwise. This direction is southwest if we consider north as 0°.

5. He walks 4√2 m in the southwest direction. This distance will be split equally between south and west due to the 45° angle of southwest. So, he walks 4m west and 4m south.

6. Now, he is 4m south and 5m west of point P.

To find the distance between points P and Q, we can use the Pythagorean theorem because the path forms a right triangle. The theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

So, the distance between P and Q = √((4m)^2 + (5m)^2) = √(16m^2 + 25m^2) = √41m^2 = approximately 6.4m.

Therefore, the distance between points P and Q is more than 6 meters.

Knowee AI · Accepted Answer