Question

if the quadrilateral is translated 4 units to the left and 5 units down what is the coordinates for point a? (4,0) (5,-1) (-1,5) (0,4)

Explanation:

Step1: Recall translation rule

For a left - shift of $x$ units and a down - shift of $y$ units, the transformation rule for a point $(x_0,y_0)$ is $(x_0 - x,y_0 - y)$. Here $x = 4$ and $y=5$.

Step2: Apply the rule

Assume the original coordinates of point A are $(3,4)$. When we translate 4 units to the left, we subtract 4 from the $x$ - coordinate: $3-4=-1$. When we translate 5 units down, we subtract 5 from the $y$ - coordinate: $4 - 5=-1$. But we don't know the original coordinates from the problem description well. In general, if the original point A has coordinates $(x,y)$, the new coordinates $(x',y')$ are given by $x'=x - 4$ and $y'=y - 5$.
Let's assume we start with a point A with coordinates $(3,4)$. Then the new coordinates are $(3 - 4,4 - 5)=(-1,-1)$. But if we assume the original point A is $(3,0)$, the new point is $(3 - 4,0 - 5)=(-1,-5)$. Without seeing the original position of A on the graph clearly, if we assume the original point A is $(3,4)$ and follow the translation rule:
The translation of a point $(x,y)$ 4 units to the left and 5 units down gives $(x-4,y - 5)$.

Answer:

We need the original coordinates of point A to give an exact answer. But if we assume the original coordinates of point A are $(3,4)$, the new coordinates are $(-1,-1)$.