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:

In a translation function \(T_{a,b}(x,y)=(x + a,y + b)\), \(a\) represents the horizontal translation (negative \(a\) means left, positive \(a\) means right) and \(b\) represents the vertical translation (negative \(b\) means down, positive \(b\) means up). For \(T_{-4,6}(x,y)\), \(a=-4\) (4 units to the left) and \(b = 6\) (6 units up).

Answer:

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