Answer:
A''' = (6,10), B'''= (2,12) and C''' = (4,4).
Explanation:
We have triangle ABC with co-ordinates A(2,3), B(4,4) and C(3,0).
Now the transformations applied to the given triangle are:
1. Translate by <-5,2> i.e. translated 5 units right and 2 units up.
So, the new co-ordinates are,
A' = (2,3) + (-5,2) = (-3,5)
B' = (4,4) + (-5,2) = (-1,6)
C' = (3,0) + (-5,2) = (-2,2)
2. Reflected across y-axis i.e. (x,y) becomes (-x,y)
The new co-ordinates are,
A'' = (-3,5) ⇒ (3,5)
B'' = (-1,6) ⇒ (1,6)
C'' = (-2,2) ⇒ (2,2)
3. Dilated by a factor of 2.
The final co-ordinates are,
A''' = 2 × (3,5) = (6,10)
B''' = 2 × (1,6) = (2,12)
C''' = 2 × (2,2) = (4,4)
Hence, the co-ordinates are given by, A'''(6,10), B'''(2,12) and C'''(4,4).