Question

identifying dilations
what scale factor that maps the preimage onto the image?
k =

Explanation:

Step1: Identify coordinates of a point

Let's take point B and B'. Assume grid size is 1 unit. Let's find their coordinates. Suppose B is at (x1,y1) and B' at (x2,y2). From the graph, let's say B is at (2, 4) and B' is at (1, 2) (assuming preimage is the larger quadrilateral, image is smaller). Wait, actually, preimage is the larger one (the outer quadrilateral), image is the inner green one. So let's take a side length. Let's check the horizontal distance from A to B in preimage and A' to B' in image. Suppose A is at (-4, 2), B at (2, 4). A' at (-2, 1), B' at (1, 2). The vector from A to B: (2 - (-4), 4 - 2) = (6, 2). From A' to B': (1 - (-2), 2 - 1) = (3, 1). So the scale factor k is the ratio of image length to preimage length. For the x - component: 3/6 = 1/2. For y - component: 1/2. So k = 1/2.

Step2: Verify with another point

Take point D and D'. Suppose D is at (-4, -2), D' at (-2, -1). Vector from D to A: (-4 - (-4), 2 - (-2)) = (0, 4). Vector from D' to A': (-2 - (-2), 1 - (-1)) = (0, 2). Ratio is 2/4 = 1/2. So scale factor k is 1/2.

Answer:

$\frac{1}{2}$