To solve this problem, we need to analyze the function rule given in the translation notation [tex]\( T_{-4,6}(x, y) \)[/tex]. The notation [tex]\( T_{-4,6} \)[/tex] indicates a translation transformation applied to any point [tex]\((x, y)\)[/tex] on the coordinate plane.
The function rule [tex]\( T_{-4,6}(x, y) \)[/tex] can be interpreted as follows:
- The first component, [tex]\(-4\)[/tex] (T_{-4}), indicates a horizontal translation. Specifically, [tex]\( -4 \)[/tex] means that we move each point 4 units to the left.
- The second component, [tex]\( 6 \)[/tex] (T_{6}), refers to a vertical translation. Specifically, [tex]\( 6 \)[/tex] means that we move each point 6 units up.
Given this information, we can determine which geometric figure and its specific translation match these descriptions. Let's review the options provided:
1. A parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right: This is incorrect because the translation here states 4 units down and 6 units to the right, which does not match our translation rule.
2. A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up: This is correct because it matches our interpretation of the translation [tex]\( T_{-4,6} \)[/tex].
3. A rhombus on a coordinate plane that is translated 4 units down and 6 units to the left: This is incorrect because the translation here mentions 4 units down and 6 units to the left, which does not match our translation rule.
4. A rectangle on a coordinate plane that is translated 4 units to the right and 6 units up: This is incorrect because the translation here mentions 4 units to the right and 6 units up, which does not match our translation rule.
Based on the translation rule [tex]\( T_{-4,6}(x, y) \)[/tex], the correct figure and translation description is:
A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up.
So, the correct answer is:
2
