Answer:
B/A = 1/2
Step-by-step explanation:
You want the scale factor between the two figures shown.
Scale factor
The scale factor is the ratio of the length in one figure to the corresponding length in the other figure. Often, we're interested in the scale factor B/A, which is what A dimensions need to be multiplied by in order to match the B dimensions.
Application
You can pick any corresponding dimensions. Often, it is convenient to choose a short one, so you don't have to count so many grid squares.
We can choose the line from the center, where the lines cross, up and to the right to the upper right corner. In the A figure, that line goes 2 squares to the right and 2 squares up. In the B figure, that line goes 1 square right and 1 square up. Then the scale factor is ...
(B dimension)/(A dimension) = 1/2
We can choose to look at the lengths of that line (A: 2√2; B: √2), or the x-dimension (A: 2; B: 1) or the y-dimension (A: 2; B: 1). All the measurements are proportional, so we get the same ratio for any pair of corresponding measures.
The scale factor B/A is 1/2.
__
Additional comment
The horizontal magenta lines in the attached figure are another possibility for determining the scale factor. B/A = 2/4 = 1/2.
You need to be careful to understand what scale factor you want. Sometimes it is described as "A to B", which can be ambiguous.
Here, the ratio of an A dimension to a B dimension is A : B = 2 : 1. The same wording can be interpreted to mean "the scale factor that multiplies A to transform it to B." That is the scale factor we have shown.
