Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle is translated 4 units down and 3 units left. Which rule represents the translation? After the translation, what are the coordinates of vertex C?

A)(x, y) → ( x + 3, y + 4); (11, 7)B)(x, y) → (x − 4, y + 3); −6, 7)C)(x, y) → ( x − 3, y − 4); (5, −1)D)(x, y) → (x − 2, y − 1); (−5, 7)

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

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

Thus, the translation is given by

The vertices of C after translation can be determined by

Thus, is the coordinates of C after translation.

Hence, Option C is the correct answer.

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