Question

use the translation rule (x, y) → (x - 8, y + 4) to answer the questions. 7. what is the image of a(2, 6)? 8. what is the pre - image of d(4, - 3)? graph △xyz with vertices x(2, 4), y(6, 0), and z(7, 2) and its image after the composition. (see example 4.) 9. translation: (x, y) → (x - 6, y) translation: (x, y) → (x + 2, y + 7) 10. describe and correct the error in graphing the image of △abc after the translation (x, y) → (x - 3, y + 2). write rules for the composition of translations. 11. 12.

Explanation:

for 7:

Step1: Apply translation to x-coordinate

$2 - 8 = -6$

Step2: Apply translation to y-coordinate

$6 + 4 = 10$

for 8:

Step1: Solve for preimage x

$x = 4 + 8 = 12$

Step2: Solve for preimage y

$y = -3 - 4 = -7$

for 9:

Step1: Compose translations

$(x-6+2, y+7)=(x-4, y+7)$

Step2: Translate X

$2-4=-2$, $4+7=11$ → $(-2,11)$

Step3: Translate Y

$6-4=2$, $0+7=7$ → $(2,7)$

Step4: Translate Z

$7-4=3$, $2+7=9$ → $(3,9)$

for 10:

Step1: Identify error

Likely incorrect direction (e.g., +3 x or -2 y)

Step2: Correct translation

Apply $(x-3,y+2)$ to each vertex

Answer:

for 7:
$(-6, 10)$