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: Understand translation rule

In the translation rule $T_{a,b}(x,y)=(x + a,y + b)$, $a$ represents the horizontal - shift and $b$ represents the vertical - shift.

Step2: Analyze the given rule

For $T_{-4,6}(x,y)$, $a=-4$ and $b = 6$. A negative value of $a$ means a left - shift and a positive value of $b$ means an up - shift. When $a=-4$, the figure is shifted 4 units to the left, and when $b = 6$, the figure is shifted 6 units up.

Answer:

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