Option C:
is the coordinates of C after translation.
Explanation:
The triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3).
Also, given that the triangle is translated 4 units down and 3 units left.
We need to determine the coordinates of the vertex C after translation.
The triangle is shifted 4 units down means subtracting 4 units from the y - coordinate of the graph.
Thus, it can be written as ![y-4](https://tex.z-dn.net/?f=y-4)
Also, the triangle is shifted 3 units left means subtracting 3 units from the x - coordinate of the graph.
Thus, it can be written as ![x-3](https://tex.z-dn.net/?f=x-3)
Thus, the translation is given by
![(x, y) \rightarrow(x-3, y-4)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%5Crightarrow%28x-3%2C%20y-4%29)
The vertices of C after translation can be determined by
![(8, 3) \rightarrow(8-3, 3-4)\implies (5,-1)](https://tex.z-dn.net/?f=%288%2C%203%29%20%5Crightarrow%288-3%2C%203-4%29%5Cimplies%20%285%2C-1%29)
Thus,
is the coordinates of C after translation.
Hence, Option C is the correct answer.