Triangle ABC with vertices A(1,1), B(2,4) and C(3,1) is rotated 90°
counterclockwise about the origin and then translated using (x, y) →
(x - 2y + 3). What are the coordinates of the final image of point C under
this composition of transformations?
A. (3,-6)
B. (-3,6)
C. (-3,1)
D. (-1,3)

The coordinates of the final image of point C under

this composition of transformations will be (-3,6).

Therefore, the option B is correct.

Step-by-step explanation:

The rule of 90 degree counterclockwise rotation about the origin

So when triangle ABC with vertices A(1,1), B(2,4) and C(3,1) is rotated 90°

counterclockwise about the origin, observe the transformation of

the point C(3,1):

P(x, y)     →      P'(-y, x)

C(3,1)      →      C'(-1,3)

And then translated using (x,y) →  (x - 2, y + 3). So,

(x,y)            →            (x - 2, y + 3)

C'(-1,3)        →            C''(-1 - 2, 3 + 3) = C''(-3, 6)

So, the coordinates of the final image of point C under

this composition of transformations will be (-3,6).

Therefore, the option B is correct.

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step-by-step explanation: