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.