Quiz 1

An angle is facing North-East direction initially, now she turns 180° in a clockwise direction. This means that now the angle is facing South-West direction. After that the angle is turned 360° in the anticlockwise direction, which implies the direction has not changed, meaning that is still facing the South-West direction. Now the angle turns another 270° in the clockwise direction. This means the angle moves towards the South-East making a 90°, North-East making a 180° and ends up in the South-East direction after the 270° clockwise turn.

The woman is facing towards North, and moving 65 degrees clockwise will make the woman point towards North West and then again 25 degrees from that means a total of 90 degrees clockwise from West.

So the woman is facing Northwards.

The man is travelling towards the South and then took a right turn means now he is facing towards the West.

From this point again he travelled 40m Northwards means he is facing towards North. And then took an about-turn of 45 degrees means he is facing towards North-West.

The child is travelling 2 km East.

Then 4 km Northwards.

Then 2 km in the West direction from that point.

And again 1 km South from that point,

Means 4 km is parallel to this 1 km to form a square.

Thus the child is 3km away from school

By applying pythogerous theorem,

1.                               = √32  + 42


2.                               = 5km, South-East.

Facing west, the boy turns 85 degrees clockwise means he is moving towards North and again 50 degrees in the same direction, which means a total of 135 degrees from West. Thus the boy is facing in North-East direction.

1. From pythogerous theorem, we can take base ‘b’ as distance traveled in the West direction which is b = 5km and height ‘h’  as distance traveled in the South direction which is h = 4 -1 km = 3km


2. By applying P.T.  slant height = √b^{2} + h^{2}           
   
   
   
   1. 
      
      
      
      1. 
         
         
         
         1. = √5^{2}  + 3^{2}
         
         
         2. √34 km
         
         
         
         
      
      
      
      
   
   
   
   

Shireen is facing North and walking 15 m leftward, which means she is walking in the West direction. She took an about-turn and walked 30 m means she turned towards East and covered 30 m in total i.e 15 (already covered) +15(towards east)

Thus Shireen is 15m away from the starting point facing eastward.

To determine the location of X with respect to his house, we need to track his movements.
X took the following steps:

6 steps towards South
5 steps towards East
8 steps towards South
5 steps towards West
6 steps towards North
6 steps towards West
steps towards North
finally 6 steps towards East.

From these steps, we can see that X moved 6 steps to the North

Therefore, the answer to the given question is 6 steps to the North.