The combined length of the original line segment and its dilated image is 30.
What is dilation?
Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.
Line segment RS is graphed with its endpoints at (1, 3) and (7, 11).
If RS is dilated by a scale factor of 2 with (4, 7) as the center of dilation.
The length of RS will be
\(\rm RS = \sqrt{(7 - 1)^2 +(11 - 3)^2}\\\\RS = \sqrt{6^2 +8^2}\\\\RS = \sqrt{64 + 36}\\\\RS = \sqrt{100}\\\\RS = 10\)
The length is dilated by the scale factor of 2.
Then the length of the dilated line segment (R'S') will be
R'S' = 10 × (2)
R'S' = 20
Then the combined length of the original line segment and its dilated image is 20 + 10 = 30.
More about the dilation link is given below.
https://brainly.com/question/2856466
