We'll look at two points on both pentagons.
Point E is located at (2,0). Point E' is located at (4,0). To find the scale factor of the dilation, divide the x and y points of the new image by the original image:
4 ÷ 2 = 2
0 ÷ 0 = 0
The y values are irrelevant to this problem, as both points are on the line x = 0. The scale factor for this dilation is 2.
Point U is located at (3,2). Point U' is located at (6,4). Divide the x and y values of the points to find the scale factor:
6 ÷ 2 = 3
4 ÷ 2 = 2
The scale factor is 2.
We can conclude that HOUSE was expanded by a scale factor of 2 to create H'O'U'S'E'.
Hope this helps.... :)