Question

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)

Answer 1

The coordinates of the final image of point C under

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

Therefore, the option B is correct.

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
  `(x,y)` to
  `(-y,x)`.

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.