Position and Direction：練習問題

A hiker is standing at the center of a park facing South. If he turns \( 135^{\circ} \) clockwise, which of the 8-point compass directions will he be facing?

A car is parked at a spot. If a library is North-West of the car and a hospital is South-West of the car, what is the direction of the hospital from the library?

An airplane starts at a point, flies 200 km North, then 200 km East, and finally 200 km South-West. In which general direction is the airplane's current position from its starting point?

A small boat is sailing East. It makes a \( 45^{\circ} \) anti-clockwise turn to avoid an obstacle. What is its new direction?

Point P is at coordinates \((5, 2)\) and Point Q is at \((5, 8)\). Point R is located such that it is East of Point Q and North-East of Point P. What are the coordinates of Point R?

On a map, the Library is North of the Park and the School is West of the Library. What is the direction of the Park from the School?

Three landmarks \( P \), \( Q \), and \( R \) are positioned such that \( Q \) is South-West of \( P \), and \( R \) is South of \( P \). If the distance \( PQ \) is equal to the distance \( PR \), what is the direction of \( Q \) from \( R \)?

An explorer is facing South. He makes a \( 225^{\circ} \) clockwise turn. In which 8-point compass direction is he facing now?

A hiker is using a compass to navigate through a forest.
(a) The hiker is currently facing West. If he turns \( 45^{\circ} \) anti-clockwise, which of the 8-point compass directions will he be facing?
(b) From the direction found in part (a), how many degrees clockwise must he turn to face North?

In a 2D coordinate system, consider a triangle with vertices at Point A \((2, 2)\), Point B \((8, 2)\), and Point C \((5, 6)\).
(a) What is the length of the base AB?
(b) What is the height of the triangle relative to base AB?
(c) If the triangle is shifted 3 units to the left and 2 units up, what are the new coordinates of Point C?