Question

Which of the following represents the translation of A (1, −2) along the vector <−5, 1> and then the vector <3, 0>?

Answers:
A (1, −2) → A ′(−5, −2) → A ″(−15, 0)
A (1, −2) → A ′(−4, −1) → A ″(−1, −1)
A (1, −2) → A ′(2, −7) → A ″(6, −7)
A (1, −2) → A ′(−5, 1) → A ″(3, 0)

Answer 1

A (1, −2) → A ′(−4, −1) → A ″(−1, −1)

Step-by-step explanation:

Use the first translation vector <−5, 1> to determine the rule for translation of the coordinates: (x, y)→(x+(−5), y+1).

Apply the rule to translate point A(1,−2).

A(1,−2)→(1+(−5),−2+1)→A'(−4,−1).

Then use the second translation vector <3, 0> to determine the rule for translation of the coordinates: (x, y)→(x+3, y+0).

Apply the rule to translate point A'(−4,−1).

A'(−4,−1)→(−4+3,−1+0)→A''(−1,−1).

Therefore, A(1,−2)→A'(−4,−1)→A''(−1,−1) represents the translation of A(1,−2) along the vector <−5, 1> and then the vector <3, 0> .

Answer 2

A (1, −2) → A ′(−4, −1) → A ″(−1, −1)

Step-by-step explanation:

(x, y)→(x+(−5), y+1).

A(1,−2).

A(1,−2)→(1+(−5),−2+1)→A'(−4,−1).

A'(−4,−1).

A'(−4,−1)→(−4+3,−1+0)→A''(−1,−1).