Answer:
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
- When we rotate a figure of 90° counterclockwise about the origin, each point of the given figure or original object gets changed from [tex](x,y)[/tex] to [tex](-y,x)[/tex].
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.
