Question

1. mike is playing a video game that involves moving a player on the coordinate plane. the player went through following translations. determine the final location of the player. a. player starts at (0, 0) b. first move → (x +7, y -4) c. second move → (x -2, y +5) d. third move → (x -4, y +1) e. fourth move → (x -3, y +4) final location: (-2,6 )

Explanation:

Step1: Calculate the final x - coordinate

The initial x - coordinate is \(x = 0\). For each move, we apply the change in x:
First move: \(x_1=0 + 7\)
Second move: \(x_2=x_1-2=(0 + 7)-2\)
Third move: \(x_3=x_2-4=((0 + 7)-2)-4\)
Fourth move: \(x_4=x_3-3=(((0 + 7)-2)-4)-3\)

Simplify the expression for \(x_4\):
\[

$$\begin{align*} x_4&=0+7 - 2-4 - 3\\ &=7-(2 + 4+3)\\ &=7 - 9\\ &=- 2 \end{align*}$$

\]

Step2: Calculate the final y - coordinate

The initial y - coordinate is \(y = 0\). For each move, we apply the change in y:
First move: \(y_1=0-4\)
Second move: \(y_2=y_1 + 5=(0-4)+5\)
Third move: \(y_3=y_2 + 1=((0-4)+5)+1\)
Fourth move: \(y_4=y_3 + 4=(((0-4)+5)+1)+4\)

Simplify the expression for \(y_4\):
\[

$$\begin{align*} y_4&=0-4 + 5+1+4\\ &=(-4)+(5 + 1+4)\\ &=-4 + 10\\ &=6 \end{align*}$$

\]

Answer:

The final location of the player is \((-2,6)\)