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(-8, 1) → r(□,□) s(-7, 4) → s(□,□) t(-3, 2) → t(□,□) (b) choose the general rule below that describes the translation mapping △rst to △rst. (x, y) → (x - 8, y + 6) (x, y) → (x + 6, y - 8) (x, y) → (-6x, 8y) (x, y) → (x + 8, y - 6) (x, y) → (-8x, 6y) (x, y) → (x - 6, y + 8)

Explanation:

Step1: Assume the translation rule is $(x,y)\to(x + a,y + b)$. Let's find $a$ and $b$ by trial - and - error or by looking at the options. Let's assume the rule is $(x,y)\to(x + 6,y - 8)$.

For point $R(-8,1)$:
$x=-8,y = 1$. New $x=-8 + 6=-2$, new $y=1-8=-7$. So $R'(-2,-7)$.

Step2: For point $S(-7,4)$:

$x=-7,y = 4$. New $x=-7 + 6=-1$, new $y=4-8=-4$. So $S'(-1,-4)$.

Step3: For point $T(-3,2)$:

$x=-3,y = 2$. New $x=-3+6 = 3$, new $y=2-8=-6$. So $T'(3,-6)$.

Step4: Check the rule in part (b).

The rule $(x,y)\to(x + 6,y - 8)$ is one of the options.

Answer:

(a)
$R'(-2,-7)$
$S'(-1,-4)$
$T'(3,-6)$
(b) $(x,y)\to(x + 6,y - 8)$