RSV has coordinates R(2, 1), S(3, 2), and V(2, 6). A translation maps points R to R' at (–4, 8). What are the coordinates for S' for this translation? (1 point) Responses
(–6, –4)
(–6, –4)
(–3, 2)
(–3, 2)
(–3, 9)
(–3, 9)
(–4, 13)
None of the answer choices provided match the coordinates for S' in the question description. Therefore, the correct answer is not provided.
To find the coordinates for S' after the translation, we can use the same translation vector that was used for R'. The translation vector represents the change in x and y coordinates from the original point to its corresponding point after the translation.
In this case, the translation vector is (-4, 8) because R was mapped to R' at (-4, 8).
To find the coordinates for S', we can add the translation vector to the coordinates of S:
Coordinates of S' = Coordinates of S + Translation vector
= (3, 2) + (-4, 8)
= (3 - 4, 2 + 8)
= (-1, 10)
Therefore, the coordinates for S' for this translation are (-1, 10).
To find the coordinates for S' after the translation, we need to translate point S(3, 2) using the same translation vector that mapped point R to R'.
Given that point R is mapped to R' at (-4, 8), we can find the translation vector by subtracting the coordinates of R' from the coordinates of R:
Translation vector = (x-coordinate of R' - x-coordinate of R, y-coordinate of R' - y-coordinate of R)
= (-4 - 2, 8 - 1)
= (-6, 7)
Now, we can apply this translation vector to point S to find the coordinates of S':
Coordinate of S' = (x-coordinate of S + x-coordinate of translation vector, y-coordinate of S + y-coordinate of translation vector)
= (3 + (-6), 2 + 7)
= (-3, 9)
Therefore, the coordinates for S' after the translation are (-3, 9).
The correct answer choice is: (–3, 9).