Question

Under the translation by the vector (4,−3), the image coordinates of the vertices for △ are ′(−1,3),′(3,−4),′(4,0). Identify the pre-image coordinates.

Answer 1

(3, - 4 ) → (3 - 4, - 4 + 3 ) → (- 1, - 1 )

(4, 0 ) → (4 - 4, 0 + 3 ) → (0, 3 )

Explanation:

to find the pre- image coordinates use the opposite vector to translate the image coordinates.

the opposite vector to (4, - 3 ) is (- 4, 3 ) , then

(- 1, 3 ) → (- 1 - 4, 3 + 3 ) → (- 5, 6 )

(3, - 4 ) → (3 - 4, - 4 + 3 ) → (- 1, - 1 )

(4, 0 ) → (4 - 4, 0 + 3 ) → (0, 3 )

Hence, the correct answers are (3, - 4 ) → (3 - 4, - 4 + 3 ) → (- 1, - 1 ),

(4, 0 ) → (4 - 4, 0 + 3 ) → (0, 3 )

Answer 2

see explanation

Explanation:

to find the pre- image coordinates use the opposite vector to translate the image coordinates.

the opposite vector to (4, - 3 ) is (- 4, 3 ) , then

(- 1, 3 ) → (- 1 - 4, 3 + 3 ) → (- 5, 6 )

(3, - 4 ) → (3 - 4, - 4 + 3 ) → (- 1, - 1 )

(4, 0 ) → (4 - 4, 0 + 3 ) → (0, 3 )