triangleRSV 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)
(–4, 13)
To find the coordinates for S' after the translation, you need to apply the same translation vector that maps R to R'.
In this case, the translation vector is (-4 - 2, 8 - 1) = (-6, 7).
To get the coordinates for S', you apply this translation vector to the coordinates of S:
(3, 2) + (-6, 7) = (-3, 9).
Therefore, the coordinates for S' are (-3, 9).
The correct answer is (–3, 9).
To find the coordinates for S' after the translation, we can use the same horizontal and vertical shift that was applied to R.
Given that R was translated to R' at (-4, 8), we need to apply the same shift to S.
The horizontal shift is -4, so we subtract 4 from the x-coordinate of S:
x-coordinate of S' = x-coordinate of S - horizontal shift
x-coordinate of S' = 3 - (-4) = 7
The vertical shift is 8, so we add 8 to the y-coordinate of S:
y-coordinate of S' = y-coordinate of S + vertical shift
y-coordinate of S' = 2 + 8 = 10
Therefore, the coordinates for S' are (7, 10).