Question

(a) the arrows below show that the coordinates on the left are mapped to the coordinates on the right. fill in the blanks to give the coordinates after the translation.
original coordinates → final coordinates
r(-7, 5) → r(-1, -4)
s(-8, 8) → s(-2, -1)
t(-4, 4) → t(2, -5)
(b) choose the general rule below that describes the translation mapping △rst to △rst.
○ (x, y) → (6x, -9y) ○ (x, y) → (x - 6, y + 9)
○ (x, y) → (x + 6, y - 9) ○ (x, y) → (x - 9, y + 6)
○ (x, y) → (9x, -6y) ○ (x, y) → (x + 9, y - 6)
○ (x, y) → (-9x, 6y) ○ (x, y) → (-6x, 9y)

Explanation:

Step1: Verify (a) coordinate translations

Check each point's x/y change:
For $R(-7,5)\to R'(-1,-4)$:
$\Delta x = -1 - (-7) = 6$, $\Delta y = -4 - 5 = -9$
For $S(-8,8)\to S'(-2,-1)$:
$\Delta x = -2 - (-8) = 6$, $\Delta y = -1 - 8 = -9$
For $T(-4,4)\to T'(2,-5)$:
$\Delta x = 2 - (-4) = 6$, $\Delta y = -5 - 4 = -9$
All (a) coordinates match this shift.

Step2: Identify general translation rule

A translation adding $\Delta x$ to $x$ and $\Delta y$ to $y$ has the form $(x,y)\to(x+\Delta x, y+\Delta y)$.
Substitute $\Delta x=6$, $\Delta y=-9$:
$(x,y)\to(x+6, y-9)$

Answer:

(a) The filled coordinates are already correct:
$R(-7, 5) \to R'(-1, -4)$
$S(-8, 8) \to S'(-2, -1)$
$T(-4, 4) \to T'(2, -5)$

(b) $\boldsymbol{(x, y) \to (x+6, y-9)}$