Given:
Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’.
To find:
The coordinates of the vertices of triangle A’B’C’.
Solution:
If triangle ABC reflected across y-axis, then
![(x,y)\to (-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28-x%2Cy%29)
![A(-1,4)\to A_1(1,4)](https://tex.z-dn.net/?f=A%28-1%2C4%29%5Cto%20A_1%281%2C4%29)
![B(-4,1)\to B_1(4,1)](https://tex.z-dn.net/?f=B%28-4%2C1%29%5Cto%20B_1%284%2C1%29)
![C(-1,1)\to C_1(1,1)](https://tex.z-dn.net/?f=C%28-1%2C1%29%5Cto%20C_1%281%2C1%29)
Coordinates of image after reflection across y-axis are ![A_1(1,4),B_1(4,1),C_1(1,1).](https://tex.z-dn.net/?f=A_1%281%2C4%29%2CB_1%284%2C1%29%2CC_1%281%2C1%29.)
Then triangle translated 4 units to the left to form triangle A’B’C’.
![(x,y)\to (x-4,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%5Cto%20%28x-4%2Cy%29)
![A_1(1,4)\to A'(-3,4)](https://tex.z-dn.net/?f=A_1%281%2C4%29%5Cto%20A%27%28-3%2C4%29)
![B_1(4,1)\to B'(0,1)](https://tex.z-dn.net/?f=B_1%284%2C1%29%5Cto%20B%27%280%2C1%29)
![C_1(1,1)\to C'(-3,1)](https://tex.z-dn.net/?f=C_1%281%2C1%29%5Cto%20C%27%28-3%2C1%29)
Therefore, the vertices of triangle A’B’C’ are A’ (-3, 4), B’ (0, 1), C’ (-3, 1).
Hence, the correct option is B.