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: Recall the translation rule

The translation rule \(T_{a,b}(x,y)=(x + a,y + b)\). Here \(a=-4\) and \(b = 6\).

Step2: Analyze the \(x\) - coordinate and \(y\) - coordinate changes

For the \(x\) - coordinate: \(x\to x+(-4)=x - 4\), which means a shift of 4 units to the left.
For the \(y\) - coordinate: \(y\to y + 6\), which means a shift of 6 units up.

Answer:

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