Question

quiz: use a model or act it out question 6 of 6 read the problem below and find the solution. use a model or act the problem out to help solve it. martha is standing on a street corner in a big city, facing south. she walks 5 blocks to the south. then, she turns right and walks 2 blocks. then, she turns right and walks 3 blocks. then, she turns right again and walks 1 block. finally, she turns left and walks 4 blocks. what direction is she facing when she is done? a. east b. west c. south d. north

Explanation:

Step1: Initial Direction

Martha starts facing south.

Step2: First Turn (Right)

Facing south, a right turn makes her face west. She walks 3 blocks west.

Step3: Second Turn (Right)

Facing west, a right turn makes her face north. She walks 2 blocks north.

Step4: Third Turn (Right)

Facing north, a right turn makes her face east. She walks 1 block east.

Step5: Fourth Turn (Left)

Facing east, a left turn makes her face north? Wait, no—wait, let's re - track: Wait, initial direction: south. First right turn from south: west (correct, because south right is west: imagine a compass, south to west is right turn). Then right turn from west: north (west right is north). Then right turn from north: east (north right is east). Then left turn from east: north? Wait, no, wait the problem says: "Then, she turns right and walks 3 blocks. Then, she turns right again and walks 2 blocks. Then, she turns right again and walks 1 block. Finally, she turns left and walks 4 blocks." Wait, I misread the turns. Let's re - do:

1. Start: facing south, walk 5 blocks south.
2. Turn right: when facing south, right turn is west. Walk 3 blocks west.
3. Turn right: facing west, right turn is north. Walk 2 blocks north.
4. Turn right: facing north, right turn is east. Walk 1 block east.
5. Turn left: facing east, left turn is north? No, wait: facing east, left turn is north? Wait, no: east left is north? Wait, compass directions: north is up, south down, east right, west left. So if you are facing east (right), left turn would be north (up). Wait, but let's use the standard: when facing a direction, right turn is 90 degrees clockwise, left is 90 degrees counter - clockwise.

Facing east: clockwise (right) is south, counter - clockwise (left) is north. Wait, I made a mistake earlier. Let's correct:

- Facing south: right turn (clockwise 90°) → west.
- Facing west: right turn (clockwise 90°) → north.
- Facing north: right turn (clockwise 90°) → east.
- Facing east: left turn (counter - clockwise 90°) → north? No, counter - clockwise from east: east to north is counter - clockwise 90°? Wait, east is right, north is up. So from east (right), turning left (towards up) is north? Wait, no: if you are facing east (looking to the right), and you turn left (towards your left, which is north). Wait, maybe a better way: use the direction sequence. The four main directions in clockwise order: north → east → south → west → north. So a right turn (clockwise) goes to the next direction in the sequence, a left turn (counter - clockwise) goes to the previous direction.

So:

- Start: south.
- Right turn (clockwise from south): next is west (south → west is clockwise? Wait, no: north (0°), east (90°), south (180°), west (270°). So a right turn (clockwise) from south (180°) is 180 + 90 = 270°, which is west. Correct.
- Right turn from west (270°): 270+90 = 360° = 0° (north). Correct.
- Right turn from north (0°): 0 + 90 = 90° (east). Correct.
- Left turn from east (90°): counter - clockwise 90°, so 90 - 90 = 0° (north)? Wait, no: counter - clockwise from east (90°) is 90 - 90 = 0° (north). Wait, but let's check the sequence: north ← west ← south ← east (counter - clockwise). So from east, left turn (counter - clockwise) is north. Wait, but let's think of a person: if you are facing east (looking right), and you turn left (towards your left), you are now facing north (looking up). Then she walks 4 blocks north? But the question is about the direction she is facing after the left turn (when she is done? Wait, the problem says "What direction is she facing when she is done?" So after the left turn and walking 4 blocks, what direction is she facing? Wait, no—when you walk in a direction, you are facing that direction. So when she turns left (while facing east) and walks 4 blocks, she is walking north, so she is facing north? Wait, no, that can't be. Wait, maybe I messed up the turns. Let's re - list all steps:

1. Initial: facing south, walk 5 blocks (direction: south, facing south).
2. Turn right: now facing west, walk 3 blocks (direction: west, facing west).
3. Turn right: now facing north, walk 2 blocks (direction: north, facing north).
4. Turn right: now facing east, walk 1 block (direction: east, facing east).
5. Turn left: now, facing east, turn left (counter - clockwise) → facing north, walk 4 blocks (direction: north, facing north).

Wait, but the options include north (D). But wait, maybe my turn directions are wrong. Let's use a different approach. Let's use the standard:

- Facing south: right turn → west (correct, because south to west is right).
- Facing west: right turn → north (correct, west to north is right).
- Facing north: right turn → east (correct, north to east is right).
- Facing east: left turn → north (correct, east to north is left).

So after the left turn, she is facing north. So the direction she is facing is north.

Answer:

D. North