Answer: The image is attached.
Step-by-step explanation:
A Dilation is defined as a transformation in which the image and the pre-image have the same shape, but their sizes are different.
When the scale factor is greater than 1, the image obtained after the dilation is greater than the pre-image and it is an "Enlargement".
When the scale factor is is between 0 and 1, the image obtained after the dilation is smaller than the pre-image and it is an "Reduction".
In this case we know that the scale factor is:

Since:

It is an Enlargement.
You can identify that the vertices of the pre-image shown in the figure, are:

So you need to multiply the coordinates of those vertices by 4 in order to get the coordinates of the image;

Now you can draw it (The image is attached).
ED = x - 5 <em>given</em>
DG = 4x - 38 <em>given</em>
ED = DG <em>definition of midpoint</em>
x - 5 = 4x - 38 <em>substitution</em>
-5 = 3x - 38 <em>subtraction property of equality (subtracted x from both sides)</em>
33 = 3x <em>addition property of equality (added 38 to both sides)</em>
11 = x <em>division property of equality (divided 3 from both sides)</em>
ED = x - 5 → ED = 11 - 5 → ED = 6 <em>substitution</em>
since ED = DG, then DG = 6 <em>transitive property</em>
ED + DG = EG <em>segment addition property</em>
6 + 6 = EG <em>substitution</em>
12 = EG <em>simplified like terms</em>
Answer: 12
Let
be the length of a leg. Using the pythagorean theorem, the hypotenuse is

So, the hypotenuse is
times as long as either leg.