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:

Step1: Analyze the \(x\) - coordinate change

In the translation rule \(T_{-4,6}(x,y)\), for the \(x\) - coordinate, we have \(x\to x + (- 4)\). A negative value for the \(x\) - translation means a shift to the left. So, the figure is translated \(4\) units to the left.

Step2: Analyze the \(y\) - coordinate change

For the \(y\) - coordinate, we have \(y\to y + 6\). A positive value for the \(y\) - translation means a shift upwards. So, the figure is translated \(6\) units up.

Answer:

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