Rectangle STUV is shown on a coordinate plane.
Rectangle STUV with vertices S at negative 7 comma 6, T at negative 2 comma 6, U at negative 2 comma 1, and V at negative 7 comma 1.
If rectangle STUV is translated using the rule (x, y) → (x − 2, y − 4) and then rotated 90° counterclockwise, what is the location of T″?
(3, −9)
(3, −4)
(−2, −4)
(−2, −9)
To find the new location of T after the translation and rotation, we first apply the translation rule of (x, y) → (x − 2, y − 4) to the coordinates of T.
T(-2, 6) translated becomes T'(-4, 2)
Now, to find the new location of T after a 90° counterclockwise rotation, we can use the rotation rule for a point (x, y) as (y, -x).
So, applying this rule to T'(-4, 2) we get:
T''(2, -4)
Therefore, the location of T'' is (2, -4).