We are going to find the coordinates of the points A'B', which are given by the dilation of AB about the point (5,5) with a scale factor of 2.
For doing so, we will determine the distance between the points A and (5,5), and we will multiply it by 2 (the scale factor). This will be the distance between A' and (5,5). We will do the same between the point B and (5,5).
As the lines x=5 and y=5 are perpendicular, the angle BPA is right (where P is the point (5,5)), we can find the distance of the point A'B' using the Pythagorean Theorem.
Now, we find the distance between A and P:
And the distance between B and P:
Multiplying by the scale factor we obtain:
And using the Pythagorean Theorem we obtain:
This means that the length of the dilation of AB will be 10.