Question

the function rule \\(t_{-4, 6}(x, y)\\) could be used to describe which translation?

a parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right
a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up
a rhombus on a coordinate plane that is translated 4 units down and 6 units to the left
a rectangle on a coordinate plane that is translated 4 units to the right and 6 units up

Explanation:

Interpret the translation notation

$$ T_{-4, 6}(x, y) = (x - 4, y + 6) $$

Analyze the coordinate shifts

$$
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$$

Match with the given options

$$ \text{Option 2: a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up} $$

Answer:

• (A) a parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right
• (B) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up (Correct answer)
• (C) a rhombus on a coordinate plane that is translated 4 units down and 6 units to the left
• (D) a rectangle on a coordinate plane that is translated 4 units to the right and 6 units up