Question

select the correct answer from each drop - down menu. quadrilateral 1 and quadrilateral 2 are polygor mapped onto each other using similarity transformations. the transformation that maps quadrilateral 1 onto quadrilateral 2 is a followed by a dilation with a scale factor of

Explanation:

Step1: Analyze the orientation of the polygons

Quadrilateral 1 and quadrilateral 2 have different orientations. A reflection can change the orientation of a polygon.

Step2: Calculate the scale factor

Let's assume a side - length of quadrilateral 1. For example, if we consider a horizontal or vertical side (by counting the grid units). Suppose a side of quadrilateral 1 has a length \(l_1\) (counting the number of units between two vertices). Let the corresponding side of quadrilateral 2 be \(l_2\).
If we count the units: assume a side of quadrilateral 1 (e.g., from \((- 6,8)\) to \((-4,6)\) has a length (using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), but for simplicity, if we consider a side that can be counted as 2 units in one - direction). A corresponding side of quadrilateral 2 (e.g., from \((2,5)\) to \((6,2)\) has a length of 4 units. The scale factor \(k=\frac{\text{length of side in quadrilateral }2}{\text{length of side in quadrilateral }1}\).
If we assume a simple side - length (by counting grid units in a non - diagonal way, for example, if we consider a side parallel to a coordinate axis after reflection). Suppose after reflection, a side of length \(a = 2\) units in quadrilateral 1 corresponds to a side of length \(b=4\) units in quadrilateral 2. The scale factor \(k=\frac{b}{a}=2\).

Answer:

reflection; 2