Question

1. what is the scale factor of the dilation from triangle a to triangle b?

Explanation:

Step1: Identify corresponding points

Take point $A(-2, 3)$ on Triangle A and its corresponding point $B(-1, 1.5)$ on Triangle B; take point $C(4, 2)$ on Triangle A and its corresponding point $D(2, 1)$ on Triangle B.

Step2: Calculate scale factor

For the x-coordinates: $\frac{-1}{-2} = \frac{1}{2}$, for the y-coordinates: $\frac{1.5}{3} = \frac{1}{2}$ (or $\frac{1}{2}$ from $\frac{1}{2}$ and $\frac{2}{4}$). The scale factor is the ratio of the coordinates of the image to the pre-image.
Expression: $\text{Scale Factor} = \frac{\text{Coordinate of Triangle B point}}{\text{Coordinate of Triangle A point}} = \frac{1}{2}$

Answer:

$\frac{1}{2}$