Question

type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar. consider figures 1 and 2 shown on the coordinate plane. figure 1 has been transformed to produce figure 2. describe the transformation. this transformation can be described by (x, y) = ( , ).

Explanation:

Step1: Analyze horizontal shift

To find the horizontal (x - direction) transformation, we can look at a corresponding point on figure 1 and figure 2. Let's take the center - like point of figure 1, say the mid - point of its base. For figure 1, if we consider a point with x - coordinate \(x = 4\) (approximate, looking at the grid), and for figure 2, the corresponding point has \(x'=- 4\). The change in x - coordinate is \(x'=x - 8\) (since \(4-8=-4\)).

Step2: Analyze vertical shift

For the vertical (y - direction) transformation, looking at the same corresponding points, the y - coordinate of the point in figure 1 and figure 2 seems to be the same (since the figures are at the same height on the grid). So the change in y - coordinate is \(y' = y+0\) (or just \(y'=y\)).

So the transformation \((x',y')=(x - 8,y)\) (assuming the vertical shift is 0, as the figures are at the same vertical level). We can also verify with other points. For example, a vertex of figure 1: if a vertex of figure 1 is at \((x = 3,y = 2)\), the corresponding vertex of figure 2 is at \((x'=3 - 8=-5,y' = 2)\), which matches the grid.

Answer:

\((x - 8,y)\) (or in the boxed form as per the question's requirement for the first box \(x - 8\) and the second box \(y\))

So the first box should have \(x-8\) and the second box should have \(y\), so the transformation is \((x',y')=(x - 8,y)\)