Question

1. if a(2, -7) translates onto a(-1, -2), then b(-4, -9) translates to b(-7, )
2. if c(-8, 9) translates onto c(-7, 8), then d(-2, 4) translates to d( , )
3. if j(6, 5) translates onto j(11, 8), then k(-7, 9) translates to k( , )

Explanation:

Step1: Find the translation rule for problem 6

For point $A(2,-7)$ translating to $A'(-1,-2)$, the change in $x$ - coordinate is $-1 - 2=-3$ and the change in $y$ - coordinate is $-2-( - 7)=5$. For point $B(-4,-9)$, the new $y$ - coordinate of $B'$ is $-9 + 5=-4$.

Step2: Find the translation rule for problem 7

For point $C(-8,9)$ translating to $C'(-7,8)$, the change in $x$ - coordinate is $-7-( - 8)=1$ and the change in $y$ - coordinate is $8 - 9=-1$. For point $D(-2,4)$, the new $x$ - coordinate of $D'$ is $-2+1=-1$ and the new $y$ - coordinate of $D'$ is $4+( - 1)=3$.

Step3: Find the translation rule for problem 8

For point $J(6,5)$ translating to $J'(11,8)$, the change in $x$ - coordinate is $11 - 6 = 5$ and the change in $y$ - coordinate is $8 - 5=3$. For point $K(-7,9)$, the new $x$ - coordinate of $K'$ is $-7 + 5=-2$ and the new $y$ - coordinate of $K'$ is $9+3 = 12$.

Answer:

1. $-4$
2. $-1,3$
3. $-2,12$