The function rule [tex]T_{-4,6}(x, y)[/tex] could be used to describe which translation?

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
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



Answer :

To determine which translation the function rule [tex]\(T_{-4,6}(x, y)\)[/tex] describes, let's break down what each component of the rule [tex]\(T_{-4,6}\)[/tex] implies.

1. The notation [tex]\(T_{-4,6}\)[/tex] represents a translation transformation in the coordinate plane.
2. Specifically, the rule [tex]\(T_{-4,6}\)[/tex] tells us how to alter the coordinates [tex]\((x, y)\)[/tex].

The components of the function rule are:
- The first number, [tex]\(-4\)[/tex], means we translate the given figure 4 units to the left (negative x-direction).
- The second number, [tex]\(6\)[/tex], means we translate the given figure 6 units up (positive y-direction).

Now let’s analyze each option one by one:

1. A parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right:
- This would correspond to [tex]\(T_{4,-6}(x, y)\)[/tex], not [tex]\(T_{-4,6}(x, y)\)[/tex]. Hence, this is incorrect.

2. A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up:
- This matches the transformation [tex]\(T_{-4,6}(x, y)\)[/tex] perfectly. Thus, this option is correct.

3. A rhombus on a coordinate plane that is translated 4 units down and 6 units to the left:
- This would correspond to [tex]\(T_{-4,-6}(x, y)\)[/tex], not [tex]\(T_{-4,6}(x, y)\)[/tex]. Hence, this is incorrect.

4. A rectangle on a coordinate plane that is translated 4 units to the right and 6 units up:
- This would correspond to [tex]\(T_{4,6}(x, y)\)[/tex], not [tex]\(T_{-4,6}(x, y)\)[/tex]. Hence, this is incorrect.

Therefore, the correct translation described by the function rule [tex]\(T_{-4,6}(x, y)\)[/tex] is the second option:

- "A trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up."