Question

In Future City, a virtual reality adventure game, you start at location P = −2.25° on the city's coordinate map. Your first mission is to reach the power-up station located at point P + d = 5.75° to gather resources. The game's hint tells you to move ∣d|degrees to the right to reach the station.How many degrees, d, did your character move to get to the power-up station? Explain how you figured out the number of degrees, using a number line, or by another method. 2 pts (NS.1c, d)

Answer 1

To determine how many degrees \( d \) your character moved to reach the power-up station, we need to start from your initial position \( P \) and find the distance \( d \) that would take you to the power-up station.

1. You start at point \( P = -2.25° \).
2. The power-up station is at point \( P + d = 5.75° \).

We can express the relationship between \( P \), \( d \), and the power-up station as: \[ P + d = 5.75° \]

Substituting the value of \( P \): \[ -2.25° + d = 5.75° \]

To find \( d \), we need to isolate it: \[ d = 5.75° + 2.25° \] \[ d = 8.00° \]

Now we need to check the direction of movement. The hint mentions to move \( |d| \) degrees to the right, which indicates that \( d \) is positive. So, moving \( 8.00° \) to the right from \(-2.25°\) lands you at \( 5.75°\):

Using a number line:

• Start at \(-2.25°\).
• Move 8 degrees to the right, reaching \( 5.75°\).

Therefore, the character moved \( d = 8.00°\) to reach the power-up station.