Which of the following represents the translation of A (1, −2) along the vector <−5, 1> and then the vector <3, 0>? A. A (1, −2) → A ′(2, −7) → A ″(6, −7)
B. A (1, −2) → A ′(−4, −1) → A ″(−1, −1)
C. A (1, −2) → A ′(−5, 1) → A ″(3, 0)
D. A (1, −2) → A ′(−5, −2) → A ″(−15, 0)

B. A (1, −2) → A ′(−4, −1) → A ″(−1, −1)

Step-by-step explanation:

When you see anything in between <> (let's say <a, b> are the numbers), it basically means <x+a, y+b>.

So if you replace a with -5, b with 1, and x and y with (1, -2) you get...

= (1 + (-5), -2 + 1)

= (1-5, -1)

= (-4, -1) > Those are the coordinates of the new point.

But wait, it says that we now have to translate along the vector <3, 0>

So (-4, -2) become the new (x, y) coordinates and <3, 0> become the new a, b

= (-4+3, -1 + 0)

= (-1, -1)

That means that the coordinates of point A'' are (-1, -1)

Another way you could do this is by combining the two translations to just do one translation. It'll skip over the middle step, but will still give you the correct answer.

You would combine them by adding the translations of the x-coordinates together and the y-coordinates together

= <-5 + 3, 1 + 0 >

= <-2, 1>

Now you translate the point by this vector and...

= (1 - 2, -2 + 1)

= (-1, -1)

Tada! It works!

Therefore, the answer is B.

12/11c

or

12

c

11