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 d(-8, 8) → d(1, -3) e(-4, 4) → e(5, -1) f(-7, 5) → f(2, 0) (b) choose the general rule below that describes the translation mapping △def to △def. ○ (x, y) → (x - 9, y + 5) ○ (x, y) → (5x, -9y) ○ (x, y) → (-5x, 9y) ○ (x, y) → (x + 5, y - 9) ○ (x, y) → (x - 5, y + 9) ○ (x, y) → (-9x, 5y) ○ (x, y) → (x + 9, y - 5) ○ (x, y) → (9x, -5y)

Explanation:

Step1: Verify x-translation for D

$1 - (-8) = 9$

Step2: Verify y-translation for D

$-3 - 8 = -11$

Step3: Verify x-translation for E

$5 - (-4) = 9$

Step4: Verify y-translation for E

$-1 - 4 = -5$

Step5: Verify x-translation for F

$2 - (-7) = 9$

Step6: Verify y-translation for F

$0 - 5 = -5$

Step7: Match rule to translations

The consistent translation is adding 9 to $x$, subtracting 5 from $y$.

Answer:

(a)
$D(-8, 8) \to D'(1, -3)$
$E(-4, 4) \to E'(5, -1)$
$F(-7, 5) \to F'(2, 0)$
(b) $\boldsymbol{(x, y) \to (x+9, y-5)}$