Question

1. a) translation: (x, y)→(x + 8, y + 1) b) translation: (x, y)→(x + 7, y + 4) c) translation: (x, y)→(x + 6, y + 2) d) translation: (x, y)→(x + 8, y + 3)

Explanation:

Step1: Select a point

Let's take point $F$. Assume $F$ has coordinates $(x_1,y_1)$ and $F'$ has coordinates $(x_2,y_2)$.

Step2: Calculate $x -$ translation

Count the horizontal units from $F$ to $F'$. If we assume $F$ is at some initial $x -$ coordinate and $F'$ is 6 units to the right. So the change in $x$ is $\Delta x=x_2 - x_1=6$.

Step3: Calculate $y -$ translation

Count the vertical units from $F$ to $F'$. The point $F'$ is 2 units above $F$. So the change in $y$ is $\Delta y=y_2 - y_1 = 2$.

Step4: Determine the translation rule

The translation rule for all points is $(x,y)\to(x + 6,y+2)$.

Answer:

C. translation: $(x,y)\to(x + 6,y+2)$