Question

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

Explanation:

Step1: Identify Coordinates

Find coordinates of preimage (e.g., A, B, C) and image (A', B', C'). Let's take point A: Preimage A is at (-2, 3), Image A' is at (-1, 1.5)? Wait, better to use horizontal/vertical lengths. Preimage triangle: base from B to C, let's count grid squares. Preimage (blue larger triangle): from x=-2 to x=2 (length 4), y from -1 to 3 (height 4)? Wait, no, looking at the graph, preimage (the larger blue triangle) has vertices, say, A(-2, 3), B(-2, -1), C(2, -1). Image (smaller blue triangle) has A'(-1, 1.5)? Wait, no, maybe better to take a side. Let's take segment AB: preimage AB length (vertical) from y=-1 to y=3, x=-2: length 4. Image A'B' (vertical) from y=0 to y=2? Wait, maybe I misread. Wait, the preimage is the larger triangle, image is the smaller one inside. Let's take point B: preimage B is at (-2, -1), image B' is at (-1, 0)? Wait, no, looking at the grid, let's count the horizontal distance from the y-axis. Preimage point C: x=2, image C' is at x=1. So the x-coordinate of C is 2, C' is 1. So scale factor k = (image length)/(preimage length) = 1/2. Let's check another point: A preimage: x=-2, image A' x=-1. So -1 / -2 = 1/2. So scale factor is 1/2.

Step2: Confirm with Lengths

Preimage side (e.g., from x=-2 to x=2: length 4). Image side (from x=-1 to x=1: length 2). So 2/4 = 1/2. So scale factor k = 1/2.

Answer:

$\frac{1}{2}$