Answer :
To determine the translation described by the function rule [tex]\( T_{-4,6}(x, y) \)[/tex], let's analyze the given transformation step by step.
1. Understanding the Notation: The transformation [tex]\( T_{-4, 6}(x, y) \)[/tex] indicates that each point [tex]\((x, y)\)[/tex] on a shape is moved to a new location. The notation [tex]\( T_{-4, 6} \)[/tex] explicitly specifies the amount and direction of translation along the x and y axes.
2. Breaking Down the Translation Rule:
- x Component: The translation rule specifies [tex]\(-4\)[/tex]. This means the shape is moved 4 units to the left along the x-axis.
- y Component: The translation rule specifies [tex]\(6\)[/tex]. This denotes moving the shape 6 units up along the y-axis.
3. Selecting the Appropriate Transformation:
- First choice: "a parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right". This does not match because the translation along the x-axis should be to the right (positive), but here it is specified as to the left (negative). Furthermore, along the y-axis, it should correspond to the translation being up (positive), but down (negative) is specified here.
- Second choice: "a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up". This perfectly matches the given translation rule: [tex]\( -4 \)[/tex] for left and [tex]\( 6 \)[/tex] for up.
- Third choice: "a rhombus on a coordinate plane that is translated 4 units down and 6 units to the left". This does not match because, although the x-component matches (left), the y-component should be up (positive) rather than down (negative).
- Fourth choice: "a rectangle on a coordinate plane that is translated 4 units to the right and 6 units up". This doesn't match because the x-component should be left (negative), but the description specifies right (positive).
Given the detailed step-by-step examination of each possible transformation description, the correct translation rule is specifically matched by:
A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up.
Therefore, the answer is:
2
1. Understanding the Notation: The transformation [tex]\( T_{-4, 6}(x, y) \)[/tex] indicates that each point [tex]\((x, y)\)[/tex] on a shape is moved to a new location. The notation [tex]\( T_{-4, 6} \)[/tex] explicitly specifies the amount and direction of translation along the x and y axes.
2. Breaking Down the Translation Rule:
- x Component: The translation rule specifies [tex]\(-4\)[/tex]. This means the shape is moved 4 units to the left along the x-axis.
- y Component: The translation rule specifies [tex]\(6\)[/tex]. This denotes moving the shape 6 units up along the y-axis.
3. Selecting the Appropriate Transformation:
- First choice: "a parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right". This does not match because the translation along the x-axis should be to the right (positive), but here it is specified as to the left (negative). Furthermore, along the y-axis, it should correspond to the translation being up (positive), but down (negative) is specified here.
- Second choice: "a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up". This perfectly matches the given translation rule: [tex]\( -4 \)[/tex] for left and [tex]\( 6 \)[/tex] for up.
- Third choice: "a rhombus on a coordinate plane that is translated 4 units down and 6 units to the left". This does not match because, although the x-component matches (left), the y-component should be up (positive) rather than down (negative).
- Fourth choice: "a rectangle on a coordinate plane that is translated 4 units to the right and 6 units up". This doesn't match because the x-component should be left (negative), but the description specifies right (positive).
Given the detailed step-by-step examination of each possible transformation description, the correct translation rule is specifically matched by:
A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up.
Therefore, the answer is:
2
