The length of segment F'G' is 7 units
Length
The length of a line segment is the number of units on the line.
Coordinates
The coordinates are given as:
[tex]F = (-2,-4)[/tex]
[tex]G = (5,-4)[/tex]
Distance
Start by calculating the length of segment FG using the following distance formula
[tex]FG = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]FG = \sqrt{(-2- 5)^2 + (-4+ 4)^2}[/tex]
[tex]FG = \sqrt{49}[/tex]
[tex]FG = 7[/tex]
The transformation of segment FG to F'G' is a rigid transformation.
This means that:
The lengths of segments FG and F'G' are the same
So, we have:
[tex]F'G' = 7[/tex]
Hence, the length of segment F'G' is 7 units
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