Question

1. translation rules

8a. a shape is translated with rule (x,y)→(x + 4,y - 2). where does point (3, - 1) move to?
a. (-1,1)
b. (7,-3)
c. (-5,7)
d. (-1,-3)
8b. apply (x,y)→(x - 6,y + 3) to point (8, - 2). new coordinates?
a. (2,1)
b. (14,-5)
c. (2,-5)
d. (-14,1)
8c. which rule translates (-3,7) to (5,4)?
a. (x,y)→(x + 8,y - 3)
b. (x,y)→(x - 8,y + 3)
c. (x,y)→(x + 3,y + 8)
d. (x,y)→(x - 3,y - 8)
8d. a figure is moved left 2 and up 5. which rule?
a. (x,y)→(x - 2,y + 5)
b. (x,y)→(x + 2,y - 5)
c. (x,y)→(x + 5,y - 2)
d. (x,y)→(x - 5,y + 2)

Explanation:

8a

Step1: Identify the translation rule

The translation rule is $(x,y)\to(x + 4,y - 2)$. Given the point $(3,-1)$, substitute $x = 3$ and $y=-1$ into the rule.

Step2: Calculate the new x - coordinate

$x_{new}=x + 4=3 + 4=7$.

Step3: Calculate the new y - coordinate

$y_{new}=y - 2=-1-2=-3$.
So the new point is $(7,-3)$.

Step1: Identify the translation rule

The translation rule is $(x,y)\to(x - 6,y + 3)$. Given the point $(8,-2)$, substitute $x = 8$ and $y = - 2$ into the rule.

Step2: Calculate the new x - coordinate

$x_{new}=x-6=8 - 6=2$.

Step3: Calculate the new y - coordinate

$y_{new}=y + 3=-2+3 = 1$.
So the new point is $(2,1)$.

Step1: Analyze the change in x and y coordinates

The point moves from $(-3,7)$ to $(5,4)$. Calculate the change in $x$: $\Delta x=5-(-3)=8$. Calculate the change in $y$: $\Delta y=4 - 7=-3$.

Step2: Determine the translation rule

The translation rule is $(x,y)\to(x + 8,y - 3)$.

Answer:

B. $(7,-3)$

8b